{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Table of Contents](./table_of_contents.ipynb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Extended Kalman Filter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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   "source": [
    "#format the book\n",
    "import book_format\n",
    "book_format.set_style()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have developed the theory for the linear Kalman filter. Then, in the last two chapters we broached the topic of using Kalman filters for nonlinear problems. In this chapter we will learn the Extended Kalman filter (EKF). The EKF handles nonlinearity by linearizing the system at the point of the current estimate, and then the linear Kalman filter is used to filter this linearized system. It was one of the very first techniques used for nonlinear problems, and it remains the most common technique. \n",
    "\n",
    "The EKF provides significant mathematical challenges to the designer of the filter; this is the most challenging chapter of the book. I do everything I can to avoid the EKF in favor of other techniques that have been developed to filter nonlinear problems. However, the topic is unavoidable; all classic papers and a majority of current papers in the field use the EKF. Even if you do not use the EKF in your own work you will need to be familiar with the topic to be able to read the literature. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linearizing the Kalman Filter\n",
    "\n",
    "The Kalman filter uses linear equations, so it does not work with nonlinear problems. Problems can be nonlinear in two ways. First, the process model might be nonlinear. An object falling through the atmosphere encounters drag which reduces its acceleration. The drag coefficient varies based on the velocity the object. The resulting behavior is nonlinear - it cannot be modeled with linear equations. Second, the measurements could be nonlinear. For example, a radar gives a range and bearing to a target. We use trigonometry, which is nonlinear, to compute the position of the target.\n",
    "\n",
    "For the linear filter we have these equations for the process and measurement models:\n",
    "\n",
    "$$\\begin{aligned}\\dot{\\mathbf x} &= \\mathbf{Ax} + w_x\\\\\n",
    "\\mathbf z &= \\mathbf{Hx} + w_z\n",
    "\\end{aligned}$$\n",
    "\n",
    "Where $\\mathbf A$ is the systems dynamic matrix. Using the state space methods covered in the **Kalman Filter Math** chapter these equations can be transformed into \n",
    "$$\\begin{aligned}\\bar{\\mathbf x} &= \\mathbf{Fx} \\\\\n",
    "\\mathbf z &= \\mathbf{Hx}\n",
    "\\end{aligned}$$\n",
    "\n",
    "where $\\mathbf F$ is the *fundamental matrix*. The noise $w_x$ and $w_z$ terms are incorporated into the matrices $\\mathbf R$ and $\\mathbf Q$. This form of the equations allow us to compute the state at step $k$ given a measurement at step $k$ and the state estimate at step $k-1$. In earlier chapters I built your intuition and minimized the math by using problems describable with Newton's equations. We know how to design $\\mathbf F$ based on high school physics.\n",
    "\n",
    "\n",
    "For the nonlinear model the linear expression $\\mathbf{Fx} + \\mathbf{Bu}$ is replaced by a nonlinear function $f(\\mathbf x, \\mathbf u)$, and the linear expression $\\mathbf{Hx}$ is replaced by a nonlinear function $h(\\mathbf x)$:\n",
    "\n",
    "$$\\begin{aligned}\\dot{\\mathbf x} &= f(\\mathbf x, \\mathbf u) + w_x\\\\\n",
    "\\mathbf z &= h(\\mathbf x) + w_z\n",
    "\\end{aligned}$$\n",
    "\n",
    "You might imagine that we could proceed by finding a new set of Kalman filter equations that optimally solve these equations. But if you remember the charts in the **Nonlinear Filtering** chapter you'll recall that passing a Gaussian through a nonlinear function results in a probability distribution that is no longer Gaussian. So this will not work.\n",
    "\n",
    "The EKF does not alter the Kalman filter's linear equations. Instead, it *linearizes* the nonlinear equations at the point of the current estimate, and uses this linearization in the linear Kalman filter. \n",
    "\n",
    "*Linearize* means what it sounds like. We find a line that most closely matches the curve at a defined point. The graph below linearizes the parabola $f(x)=x^2-2x$ at $x=1.5$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import kf_book.ekf_internal as ekf_internal\n",
    "ekf_internal.show_linearization()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If the curve above is the process model, then the dotted lines shows the linearization of that curve for the estimate $x=1.5$.\n",
    "\n",
    "We linearize systems by taking the derivative, which finds the slope of a curve:\n",
    "\n",
    "$$\\begin{aligned}\n",
    "f(x) &= x^2 -2x \\\\\n",
    "\\frac{df}{dx} &= 2x - 2\n",
    "\\end{aligned}$$\n",
    "\n",
    "and then evaluating it at $x$:\n",
    "\n",
    "$$\\begin{aligned}m &= f'(x=1.5) \\\\&= 2(1.5) - 2 \\\\&= 1\\end{aligned}$$ \n",
    "\n",
    "Linearizing systems of differential equations is similar. We linearize $f(\\mathbf x, \\mathbf u)$, and $h(\\mathbf x)$ by taking the partial derivatives of each to evaluate $\\mathbf F$ and $\\mathbf H$ at the point $\\mathbf x_t$ and $\\mathbf u_t$. We call the partial derivative of a matrix the [*Jacobian*](https://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant). This gives us the the discrete state transition matrix and measurement model matrix:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\mathbf F \n",
    "&= {\\frac{\\partial{f(\\mathbf x_t, \\mathbf u_t)}}{\\partial{\\mathbf x}}}\\biggr|_{{\\mathbf x_t},{\\mathbf u_t}} \\\\\n",
    "\\mathbf H &= \\frac{\\partial{h(\\bar{\\mathbf x}_t)}}{\\partial{\\bar{\\mathbf x}}}\\biggr|_{\\bar{\\mathbf x}_t} \n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "This leads to the following equations for the EKF. I put boxes around the differences from the linear filter:\n",
    "\n",
    "$$\\begin{array}{l|l}\n",
    "\\text{linear Kalman filter} & \\text{EKF} \\\\\n",
    "\\hline \n",
    "& \\boxed{\\mathbf F = {\\frac{\\partial{f(\\mathbf x_t, \\mathbf u_t)}}{\\partial{\\mathbf x}}}\\biggr|_{{\\mathbf x_t},{\\mathbf u_t}}} \\\\\n",
    "\\mathbf{\\bar x} = \\mathbf{Fx} + \\mathbf{Bu} & \\boxed{\\mathbf{\\bar x} = f(\\mathbf x, \\mathbf u)}  \\\\\n",
    "\\mathbf{\\bar P} = \\mathbf{FPF}^\\mathsf{T}+\\mathbf Q  & \\mathbf{\\bar P} = \\mathbf{FPF}^\\mathsf{T}+\\mathbf Q \\\\\n",
    "\\hline\n",
    "& \\boxed{\\mathbf H = \\frac{\\partial{h(\\bar{\\mathbf x}_t)}}{\\partial{\\bar{\\mathbf x}}}\\biggr|_{\\bar{\\mathbf x}_t}} \\\\\n",
    "\\textbf{y} = \\mathbf z - \\mathbf{H \\bar{x}} & \\textbf{y} = \\mathbf z - \\boxed{h(\\bar{x})}\\\\\n",
    "\\mathbf{K} = \\mathbf{\\bar{P}H}^\\mathsf{T} (\\mathbf{H\\bar{P}H}^\\mathsf{T} + \\mathbf R)^{-1} & \\mathbf{K} = \\mathbf{\\bar{P}H}^\\mathsf{T} (\\mathbf{H\\bar{P}H}^\\mathsf{T} + \\mathbf R)^{-1} \\\\\n",
    "\\mathbf x=\\mathbf{\\bar{x}} +\\mathbf{K\\textbf{y}} & \\mathbf x=\\mathbf{\\bar{x}} +\\mathbf{K\\textbf{y}} \\\\\n",
    "\\mathbf P= (\\mathbf{I}-\\mathbf{KH})\\mathbf{\\bar{P}} & \\mathbf P= (\\mathbf{I}-\\mathbf{KH})\\mathbf{\\bar{P}}\n",
    "\\end{array}$$\n",
    "\n",
    "We don't normally use $\\mathbf{Fx}$ to propagate the state for the EKF as the linearization causes inaccuracies. It is typical to compute $\\bar{\\mathbf x}$ using a suitable numerical integration technique such as Euler or Runge Kutta. Thus I wrote $\\mathbf{\\bar x} = f(\\mathbf x, \\mathbf u)$. For the same reasons we don't use $\\mathbf{H\\bar{x}}$ in the computation for the residual, opting for the more accurate $h(\\bar{\\mathbf x})$.\n",
    "\n",
    "I think the easiest way to understand the EKF is to start off with an example. Later you may want to come back and reread this section."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Tracking a Airplane\n",
    "\n",
    "This example tracks an airplane using ground based radar. We implemented a UKF for this problem in the last chapter. Now we will implement an EKF for the same problem so we can compare both the filter performance and the level of effort required to implement the filter.\n",
    "\n",
    "Radars work by emitting a beam of radio waves and scanning for a return bounce. Anything in the beam's path will reflects some of the signal back to the radar. By timing how long it takes for the reflected signal to get back to the radar the system can compute the *slant distance* - the straight line distance from the radar installation to the object.\n",
    "\n",
    "The relationship between the radar's slant range distance $r$ and elevation angle $\\epsilon$ with the horizontal position $x$ and altitude $y$ of the aircraft is illustrated in the figure below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ekf_internal.show_radar_chart()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This gives us the equalities:\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\epsilon &= \\tan^{-1} \\frac y x\\\\\n",
    "r^2 &= x^2 + y^2\n",
    "\\end{aligned}$$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Design the State Variables\n",
    "\n",
    "We want to track the position of an aircraft assuming a constant velocity and altitude, and measurements of the slant distance to the aircraft. That means we need 3 state variables - horizontal distance, horizontal velocity, and altitude:\n",
    "\n",
    "$$\\mathbf x = \\begin{bmatrix}\\mathtt{distance} \\\\\\mathtt{velocity}\\\\ \\mathtt{altitude}\\end{bmatrix}=    \\begin{bmatrix}x \\\\ \\dot x\\\\ y\\end{bmatrix}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Design the Process Model\n",
    "\n",
    "We assume a Newtonian, kinematic system for the aircraft. We've used this model in previous chapters, so by inspection you may recognize that we want\n",
    "\n",
    "$$\\mathbf F = \\left[\\begin{array}{cc|c} 1 & \\Delta t & 0\\\\\n",
    "0 & 1 & 0 \\\\ \\hline\n",
    "0 & 0 & 1\\end{array}\\right]$$\n",
    "\n",
    "I've partioned the matrix into blocks to show the upper left block is a constant velocity model for $x$, and the lower right block is a constant position model for $y$.\n",
    "\n",
    "However, let's practice finding these matrices. We model systems with a set of differential equations. We need an equation in the form \n",
    "\n",
    "$$\\dot{\\mathbf x} = \\mathbf{Ax} + \\mathbf{w}$$\n",
    "where $\\mathbf{w}$ is the system noise. \n",
    "\n",
    "The variables $x$ and $y$ are independent so we can compute them separately. The differential equations for motion in one dimension are:\n",
    "\n",
    "$$\\begin{aligned}v &= \\dot x \\\\\n",
    "a &= \\ddot{x} = 0\\end{aligned}$$\n",
    "\n",
    "Now we put the differential equations into state-space form. If this was a second or greater order differential system we would have to first reduce them to an equivalent set of first degree equations. The equations are first order, so we put them in state space matrix form as\n",
    "\n",
    "$$\\begin{aligned}\\begin{bmatrix}\\dot x \\\\ \\ddot{x}\\end{bmatrix} &= \\begin{bmatrix}0&1\\\\0&0\\end{bmatrix} \\begin{bmatrix}x \\\\ \n",
    "\\dot x\\end{bmatrix} \\\\ \\dot{\\mathbf x} &= \\mathbf{Ax}\\end{aligned}$$\n",
    "where $\\mathbf A=\\begin{bmatrix}0&1\\\\0&0\\end{bmatrix}$. \n",
    "\n",
    "Recall that $\\mathbf A$ is the *system dynamics matrix*. It describes a set of linear differential equations. From it we must compute the state transition matrix $\\mathbf F$. $\\mathbf F$ describes a discrete set of linear equations which compute $\\mathbf x$ for a discrete time step $\\Delta t$.\n",
    "\n",
    "A common way to compute $\\mathbf F$ is to use the power series expansion of the matrix exponential:\n",
    "\n",
    "$$\\mathbf F(\\Delta t) = e^{\\mathbf A\\Delta t} = \\mathbf{I} + \\mathbf A\\Delta t  + \\frac{(\\mathbf A\\Delta t)^2}{2!} + \\frac{(\\mathbf A \\Delta t)^3}{3!} + ... $$\n",
    "\n",
    "\n",
    "$\\mathbf A^2 = \\begin{bmatrix}0&0\\\\0&0\\end{bmatrix}$, so all higher powers of $\\mathbf A$ are also $\\mathbf{0}$. Thus the power series expansion is:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\mathbf F &=\\mathbf{I} + \\mathbf At + \\mathbf{0} \\\\\n",
    "&= \\begin{bmatrix}1&0\\\\0&1\\end{bmatrix} + \\begin{bmatrix}0&1\\\\0&0\\end{bmatrix}\\Delta t\\\\\n",
    "\\mathbf F &= \\begin{bmatrix}1&\\Delta t\\\\0&1\\end{bmatrix}\n",
    "\\end{aligned}$$\n",
    "\n",
    "This is the same result used by the kinematic equations! This exercise was unnecessary other than to illustrate finding the state transition matrix from linear differential equations. We will conclude the chapter with an example that will require the use of this technique."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Design the Measurement Model\n",
    "\n",
    "The measurement function takes the state estimate of the prior $\\bar{\\mathbf x}$ and turn it into a measurement of the slant range distance. We use the Pythagorean theorem to derive:\n",
    "\n",
    "$$h(\\bar{\\mathbf x}) = \\sqrt{x^2 + y^2}$$\n",
    "\n",
    "The relationship between the slant distance and the position on the ground is nonlinear due to the square root. We linearize it by evaluating its partial derivative at $\\mathbf x_t$:\n",
    "\n",
    "$$\n",
    "\\mathbf H = \\frac{\\partial{h(\\bar{\\mathbf x})}}{\\partial{\\bar{\\mathbf x}}}\\biggr|_{\\bar{\\mathbf x}_t}\n",
    "$$\n",
    "\n",
    "The partial derivative of a matrix is called a Jacobian, and takes the form \n",
    "\n",
    "$$\\frac{\\partial \\mathbf H}{\\partial \\bar{\\mathbf x}} = \n",
    "\\begin{bmatrix}\n",
    "\\frac{\\partial h_1}{\\partial x_1} & \\frac{\\partial h_1}{\\partial x_2} &\\dots \\\\\n",
    "\\frac{\\partial h_2}{\\partial x_1} & \\frac{\\partial h_2}{\\partial x_2} &\\dots \\\\\n",
    "\\vdots & \\vdots\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "In other words, each element in the matrix is the partial derivative of the function $h$ with respect to the $x$ variables. For our problem we have\n",
    "\n",
    "$$\\mathbf H = \\begin{bmatrix}{\\partial h}/{\\partial x} & {\\partial h}/{\\partial \\dot{x}} & {\\partial h}/{\\partial y}\\end{bmatrix}$$\n",
    "\n",
    "Solving each in turn:\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\frac{\\partial h}{\\partial x} &= \\frac{\\partial}{\\partial x} \\sqrt{x^2 + y^2} \\\\\n",
    "&= \\frac{x}{\\sqrt{x^2 + y^2}}\n",
    "\\end{aligned}$$\n",
    "\n",
    "and\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\frac{\\partial h}{\\partial \\dot{x}} &=\n",
    "\\frac{\\partial}{\\partial \\dot{x}} \\sqrt{x^2 + y^2} \\\\ \n",
    "&= 0\n",
    "\\end{aligned}$$\n",
    "\n",
    "and\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\frac{\\partial h}{\\partial y} &= \\frac{\\partial}{\\partial y} \\sqrt{x^2 + y^2} \\\\ \n",
    "&= \\frac{y}{\\sqrt{x^2 + y^2}}\n",
    "\\end{aligned}$$\n",
    "\n",
    "giving us \n",
    "\n",
    "$$\\mathbf H = \n",
    "\\begin{bmatrix}\n",
    "\\frac{x}{\\sqrt{x^2 + y^2}} & \n",
    "0 &\n",
    "&\n",
    "\\frac{y}{\\sqrt{x^2 + y^2}}\n",
    "\\end{bmatrix}$$\n",
    "\n",
    "This may seem daunting, so step back and recognize that all of this math is doing something very simple. We have an equation for the slant range to the airplane which is nonlinear. The Kalman filter only works with linear equations, so we need to find a linear equation that approximates $\\mathbf H$. As we discussed above, finding the slope of a nonlinear equation at a given point is a good approximation. For the Kalman filter, the 'given point' is the state variable $\\mathbf x$ so we need to take the derivative of the slant range with respect to $\\mathbf x$. For the linear Kalman filter $\\mathbf H$ was a constant that we computed prior to running the filter. For the EKF $\\mathbf H$ is updated at each step as the evaluation point $\\bar{\\mathbf x}$ changes at each epoch.\n",
    "\n",
    "To make this more concrete, let's now write a Python function that computes the Jacobian of $h$ for this problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import sqrt\n",
    "def HJacobian_at(x):\n",
    "    \"\"\" compute Jacobian of H matrix at x \"\"\"\n",
    "\n",
    "    horiz_dist = x[0]\n",
    "    altitude   = x[2]\n",
    "    denom = sqrt(horiz_dist**2 + altitude**2)\n",
    "    return array ([[horiz_dist/denom, 0., altitude/denom]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, let's provide the code for $h(\\bar{\\mathbf x})$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def hx(x):\n",
    "    \"\"\" compute measurement for slant range that\n",
    "    would correspond to state x.\n",
    "    \"\"\"\n",
    "    \n",
    "    return (x[0]**2 + x[2]**2) ** 0.5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's write a simulation for our radar."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy.random import randn\n",
    "import math\n",
    "\n",
    "class RadarSim:\n",
    "    \"\"\" Simulates the radar signal returns from an object\n",
    "    flying at a constant altityude and velocity in 1D. \n",
    "    \"\"\"\n",
    "    \n",
    "    def __init__(self, dt, pos, vel, alt):\n",
    "        self.pos = pos\n",
    "        self.vel = vel\n",
    "        self.alt = alt\n",
    "        self.dt = dt\n",
    "        \n",
    "    def get_range(self):\n",
    "        \"\"\" Returns slant range to the object. Call once \n",
    "        for each new measurement at dt time from last call.\n",
    "        \"\"\"\n",
    "        \n",
    "        # add some process noise to the system\n",
    "        self.vel = self.vel  + .1*randn()\n",
    "        self.alt = self.alt + .1*randn()\n",
    "        self.pos = self.pos + self.vel*self.dt\n",
    "    \n",
    "        # add measurement noise\n",
    "        err = self.pos * 0.05*randn()\n",
    "        slant_dist = math.sqrt(self.pos**2 + self.alt**2)\n",
    "        \n",
    "        return slant_dist + err"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Design Process and Measurement Noise\n",
    "\n",
    "The radar measures the range to a target. We will use $\\sigma_{range}= 5$ meters for the noise. This gives us\n",
    "\n",
    "$$\\mathbf R = \\begin{bmatrix}\\sigma_{range}^2\\end{bmatrix} = \\begin{bmatrix}25\\end{bmatrix}$$\n",
    "\n",
    "\n",
    "The design of $\\mathbf Q$ requires some discussion. The state $\\mathbf x= \\begin{bmatrix}x & \\dot x & y\\end{bmatrix}^\\mathtt{T}$. The first two elements are position (down range distance) and velocity, so we can use `Q_discrete_white_noise` noise to compute the values for the upper left hand side of $\\mathbf Q$. The third element of  $\\mathbf x$ is altitude, which we are assuming is independent of the down range distance. That leads us to a block design of $\\mathbf Q$ of:\n",
    "\n",
    "$$\\mathbf Q = \\begin{bmatrix}\\mathbf Q_\\mathtt{x} & 0 \\\\ 0 & \\mathbf Q_\\mathtt{y}\\end{bmatrix}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementation\n",
    "\n",
    "`FilterPy` provides the class `ExtendedKalmanFilter`. It works similarly to the `KalmanFilter` class we have been using, except that it allows you to provide a function that computes the Jacobian of $\\mathbf H$ and the function $h(\\mathbf x)$. \n",
    "\n",
    "We start by importing the filter and creating it. The dimension of `x` is 3 and `z` has dimension 1.\n",
    "\n",
    "```python\n",
    "from filterpy.kalman import ExtendedKalmanFilter\n",
    "\n",
    "rk = ExtendedKalmanFilter(dim_x=3, dim_z=1)\n",
    "```\n",
    "We create the radar simulator:\n",
    "```python\n",
    "radar = RadarSim(dt, pos=0., vel=100., alt=1000.)\n",
    "```\n",
    "We will initialize the filter near the airplane's actual position:\n",
    "\n",
    "```python\n",
    "rk.x = array([radar.pos, radar.vel-10, radar.alt+100])\n",
    "```\n",
    "\n",
    "We assign the system matrix using the first term of the Taylor series expansion we computed above:\n",
    "\n",
    "```python\n",
    "dt = 0.05\n",
    "rk.F = eye(3) + array([[0, 1, 0],\n",
    "                       [0, 0, 0],\n",
    "                       [0, 0, 0]])*dt\n",
    "```\n",
    "\n",
    "After assigning reasonable values to $\\mathbf R$, $\\mathbf Q$, and $\\mathbf P$ we can run the filter with a simple loop. We pass the functions for computing the Jacobian of $\\mathbf  H$ and $h(x)$ into the `update` method.\n",
    "\n",
    "```python\n",
    "for i in range(int(20/dt)):\n",
    "    z = radar.get_range()\n",
    "    rk.update(array([z]), HJacobian_at, hx)\n",
    "    rk.predict()\n",
    "```\n",
    "\n",
    "Adding some boilerplate code to save and plot the results we get:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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7Y/DgwRUeJ4oiBEGosHz+/PmYM2eO7nV+fj68vb0RGhoKW1vbOn0PVaFSqRAWFoYhQ4ZAJpM1+PUrIooifrx5BGkFCrgEdkcvf0djh2Sgsdbdg4L1V3Osu5pj3dUO66/mWHe1w/qrOWPVXVlvmKpotElBcXEx3n33XWzZsgWPPvooAKB9+/a4cOECvvjiCwwePBhubm5QKpXIycnRay1IT09Hr169Kjy3mZkZzMzMDLbLZDKj3uTGvn55urVwxI6LyYhILkC/Nm7GDqdCjbHuHiSsv5pj3dUc6652WH81x7qrHdZfzTV03VXnWo12nYKy/v0SiX6IUqkUGo0GABASEgKZTKbXFJOSkoLLly9XmhRQ1QV7altOIpLyjBwJEREREdUXo7YUFBYWIjo6Wvc6JiYGFy5cgIODA5o3b45+/frhrbfegoWFBXx8fHD48GH89ttv+PLLLwEAdnZ2mD59OubOnQtHR0c4ODjgzTffRHBwcKXdi6jqgjztAACXk6re/EREREREDxajJgVnzpzBgAEDdK/L+vlPmTIFa9euxYYNGzB//nw888wzyM7Oho+PDz7++GO89NJLumOWL18OExMTjBs3DsXFxRg0aBDWrl0LqbQRj4p9gJQlBUm5xcguUsLBytTIERERERFRXTNqUtC/f3+IolhhuZubG3755ZdKz2Fubo5Vq1Zh1apVdR0eAbA1l8HX0RKxWXJEJOWhXytnY4dERERERHWs0Y4poMbjThcijisgIiIiehgxKaD7CmZSQERERPRQY1JA91WWFFxKZFJARERE9DBiUkD3FexlB6lEQFJuMRKyq74yHhERERE9GJgU0H3ZmMsQ4qNdHO5QVLqRoyEiIiKiusakgKqkf2vtrEMHozKMHAkRERER1TUmBVQlA1q7AACO3cxEiUpt5GiIiIiIqC4xKaAqaeNmAzdbc5SoNDgZk23scIiIiIioDjEpoCoRBAED2mi7EC3ZcQVxWUVGjoiIiIiI6gqTAqqyl/r5w93OHLcyivD4N8cQk8nEgIiIiOhhwKSAqszH0QrbXu2NQHdbZBUpMfWXU8gqVBg7LCIiIiKqJSYFVC0utub49blu8HawQFyWHPM2XjJ2SERERERUS0wKqNqcbczw05SukEoEHIhMx9m4HGOHRERERES1wKSAaqSVqw2e6OwJAFix/7qRoyEiIiKi2mBSQDU2a2BLyKQCjt7IxClOU0pERET0wGJSQDXm7WCJcV28AQDL9kVBFEUjR0RERERENcGkgGrl1QEBMJVKcDImG8duZhk7HCIiIiKqASYFVCsezSwwsXtzAMDHu66hUFFq5IiIiIiIqLqYFFCtvdLfH3YWMlxNyceUn08xMSAiIiJ6wDApoFpzsTXHuundYWtugrNxOfi/E3HGDomIiIiIqoFJAdWJYC87vNjPHwAQlVpg5GiIiIiIqDqYFFCd8XG0BADEZ8uNHAkRERERVQeTAqozzR20SUEckwIiIiKiBwqTAqozPg5WAICMAgXkSg42JiIiInpQMCmgOmNnKYOdhQwAkJBdbORoiIiIiKiqmBRQnSobVxCXVWTkSIiIiIioqpgUUJ3yduBgYyIiIqIHjUl1dhZFEYcPH8bRo0cRGxsLuVwOZ2dndOrUCYMHD4a3t3d9xUkPCB8mBUREREQPnCq1FBQXF2Pp0qXw9vbG8OHDsWvXLuTm5kIqlSI6OhqLFi2Cn58fRowYgRMnTtR3zNSI3ek+xKSAiIiI6EFRpZaCVq1aoXv37lizZg2GDh0KmUxmsE9cXBzWr1+P8ePH4/3338eMGTPqPFhq/JrfnoGILQVERERED44qJQW7d+9GUFBQpfv4+Phg/vz5mDt3LuLi4uokOHrwNL/dUpCYI4daI0IqEYwcERERERHdT5W6D90vIbibqakpWrZsWeOA6MHmbmsOS1MpVGoRkan5xg6HiIiIiKqg2rMP7dmzB+Hh4brXX3/9NTp27IiJEyciJyenToOjB49EIqB3gBMA4N9r6UaOhoiIiIiqotpJwVtvvYX8fO0nwBEREZg7dy5GjBiBW7duYc6cOXUeID14BrVxAQDsj2RSQERERPQgqNaUpAAQExODwMBAAMCmTZswcuRILF26FOfOncOIESPqPEB68Ay8nRRcTMhFRoECzjZmRo6IiIiIiCpT7ZYCU1NTyOXamWX279+P0NBQAICDg4OuBYGaNhdbc7T3sgMAHGRrAREREVGjV+2koE+fPpgzZw4+/PBDnDp1Co8++igA4Pr16/Dy8qrzAOnBVNZacOg6kwIiIiKixq7aScHq1athYmKCjRs34ttvv4WnpycA7bSlw4YNq/MA6cHUzc8BAHAxIc/IkRARERHR/VR5TMG+ffswYMAANG/eHDt37jQoX758eZ0GRg+2IE9t96Gk3GJkFynhYGVq5IiIiIiIqCJVbil46aWX4OzsjPHjx+OPP/5AXh4/AaaK2ZrL0MJJu7pxRBLvFSIiIqLGrMpJwa1bt3DkyBEEBwdj+fLlcHV1xaBBg7By5UrExsbWY4j0oAq+Pdg4IjHXuIEQERERUaWqNaagffv2eP/993Hq1CncunULTz31FPbs2YO2bduiQ4cOWLhwIc6cOVNfsdIDJvh2F6JLiWwpICIiImrMqj3QuIyHhwdeeukl/PPPP8jMzMSCBQsQGxuLYcOGYenSpVU6x5EjRzBq1Ch4eHhAEARs3brVYJ9r165h9OjRsLOzg42NDXr06IH4+HhduUKhwKxZs+Dk5AQrKyuMHj0aiYmJNX1bVIfaezUDwO5DRERERI1djZOCu1lZWeHJJ5/Eb7/9hvT0dMyYMaNKxxUVFaFDhw5YvXp1ueU3b95Enz590KZNGxw6dAgXL17EggULYG5urttn9uzZ2LJlCzZs2IDw8HAUFhZi5MiRUKvVdfHWqBbaedhCEICUvBKkF5QYOxwiIiIiqkC1VzQGgFOnTuHQoUNIT0+HRqPRbRcEAcuWLYOzs3OVzjN8+HAMHz68wvL33nsPI0aMwOeff67b1qJFC93XeXl5+Omnn/D7779j8ODBAIB169bB29sb+/fvx9ChQ6v71qgOWZmZoKWLNa6nFeJ0TA4ebe9u7JCIiIiIqBzVTgqWLl2K999/H61bt4arqysEQdCV3f11bWk0GuzatQvz5s3D0KFDcf78efj5+WH+/PkYO3YsAODs2bNQqVS6VZUBbbemoKAgHDt2rMKkQKFQQKFQ6F6XrcSsUqmgUqnq7D1UVdk1jXHt+vZISydcTyvEnsvJCG3rVOfnf5jrriGw/mqOdVdzrLvaYf3VHOuudlh/NWesuqvO9QRRFMXqnNzV1RWfffYZpk6dWt24Kg9EELBlyxbdA39qairc3d1haWmJjz76CAMGDMCePXvw7rvv4uDBg+jXrx/Wr1+PadOm6T3gA0BoaCj8/Pzw3XfflXutxYsXY8mSJQbb169fD0tLyzp9X01dTAGw4rIJzKUiPu6ihkmddFgjIiIiovuRy+WYOHEi8vLyYGtrW+m+1W4pkEgk6N27d42Dq6qybkljxozBG2+8AQDo2LEjjh07hjVr1qBfv34VHiuKYqWtFvPnz8ecOXN0r/Pz8+Ht7Y3Q0ND7Vlh9UKlUCAsLw5AhQyCTyRr8+vVJoxGxPu4I0gsUsGvVFf1aVa1rWVU9zHXXEFh/Nce6qznWXe2w/mqOdVc7rL+aM1bdlfWGqYpqJwVvvPEGvv76a6xYsaK6h1aLk5MTTExMEBgYqLe9bdu2CA8PBwC4ublBqVQiJycH9vb2un3S09PRq1evCs9tZmYGMzMzg+0ymcyoN7mxr19fhrZzw+8n4rDnagYGt/Ool2s8rHXXUFh/Nce6qznWXe2w/mqOdVc7rL+aa+i6q861qp0UvPnmm3j00Ufh7++PwMBAg4tt3ry5uqcsl6mpKbp27YqoqCi97devX4ePjw8AICQkBDKZDGFhYRg3bhwAICUlBZcvX9YbnEzGNTxYmxRsPJsImVSCJaPbwZT9iIiIiIgajWonBbNmzcLBgwcxYMAAODo61mpwcWFhIaKjo3WvY2JicOHCBTg4OKB58+Z46623MH78eDzyyCO6MQU7duzAoUOHAAB2dnaYPn065s6dC0dHRzg4OODNN99EcHCwbjYiMr6eLRzx2sAArDoYjT9OxSPAxRrT+/gZOywiIiIiuq3aScFvv/2GTZs24dFHH631xc+cOYMBAwboXpf1858yZQrWrl2Lxx57DGvWrMEnn3yC1157Da1bt8amTZvQp08f3THLly+HiYkJxo0bh+LiYgwaNAhr166FVCqtdXxUNwRBwJzQ1rA2N8HSfyKxOyKFSQERERFRI1LtpMDBwQH+/v51cvH+/fvjfpMfPffcc3juuecqLDc3N8eqVauwatWqOomJ6s/I9h5Y+k8kzsbnICq1AH+dScCErt5o6Wpj7NCIiIiImrRqd+xevHgxFi1aBLlcXh/x0EPMo5kF2nnYQhSBcd8dx0/hMXh3S4SxwyIiIiJq8qrdUrBy5UrcvHkTrq6u8PX1NRhofO7cuToLjh4+QwJdcSU5H3nF2sU0Tsfm4HJSHoI87YwcGREREVHTVe2koGxxMaKaGBLoihX7bwAAnKzNkFmowC//xWLZuA5GjoyIiIio6ap2UrBo0aL6iIOaiEB3W0zq4YNSjQZPhnjhiW+PY8fFZLw7og0crQ3XjiAiIiKi+lftpKAq7reiMDVdgiDgw7FButftPGxxJTkf+66m4eluzY0YGREREVHTVaWBxm3btsX69euhVCor3e/GjRt4+eWX8dlnn9VJcPTwG9bODQAQdjXNyJEQERERNV1Vain4+uuv8fbbb+PVV19FaGgounTpAg8PD5ibmyMnJwdXr15FeHg4rl69ipkzZ+KVV16p77jpIRHazg3Lwq4jPDoTRYpSWJnVS+MVEREREVWiSk9gAwcOxOnTp3Hs2DH8+eefWL9+PWJjY1FcXAwnJyd06tQJkydPxrPPPotmzZrVc8j0MGnlao3mDpaIz5bjyPUMDA92N3ZIRERERE1OtT6W7dWrF3r16lVfsVATJAgCQgNd8WN4DMKupjEpICIiIjKCai9eRlTXBrZ1AQAcu5ll5EiIiIiImiYmBWR0HbyaQSIAqfklSM0rMXY4RERERE0OkwIyOiszE7RytQEAXEjINW4wRERERE0QkwJqFDp6NwMAXEzMNWocRERERE0RkwJqFHRJAVsKiIiIiBpctZOC/v3747fffkNxcXF9xENNVIfbScGlxDyoNaJxgyEiIiJqYqqdFISEhGDevHlwc3PDjBkzcOLEifqIi5qYVq42sDSVolBRilsZhcYOh4iIiKhJqXZSsGzZMiQlJeG3335DRkYGHnnkEQQGBuKLL75AWlpafcRITYBUIiDI0w4ABxsTERERNbQajSmQSqUYM2YMtm7diqSkJEycOBELFiyAt7c3xo4di3///beu46QmoJ2HLQAgMrXAyJEQERERNS21Gmh86tQpLFy4EF988QVcXFwwf/58uLi4YNSoUXjzzTfrKkZqItq6aZOCKCYFRERERA3KpLoHpKen4/fff8cvv/yCGzduYNSoUdiwYQOGDh0KQRAAAOPGjcPYsWPxxRdf1HnA9PBq7aZdqyAyNd/IkRARERE1LdVOCry8vODv74/nnnsOU6dOhbOzs8E+3bp1Q9euXeskQGo6WrnaQBCAzEIlMgoUcLYxM3ZIRERERE1CtZOCAwcOoG/fvpXuY2tri4MHD9Y4KGqaLEyl8HW0QkxmEaJSC5gUEBERETWQao8pWLRoEXJzcw225+fnY+DAgXUREzVhbdiFiIiIiKjBVTspOHz4MJRKpcH2kpISHD16tE6CoqbrzrgCDjYmIiIiaihV7j506dIlAIAoirh69SpSU1N1ZWq1Gnv27IGnp2fdR0hNSllLAWcgIiIiImo4VU4KOnbsCEEQIAhCud2ELCwssGrVqjoNjpqeNrenJb2eVgC1RoRUIhg5IiIiIqKHX5WTgpiYGIiiiBYtWuDUqVN6sw6ZmprCxcUFUqm0XoKkpqO5gyUsZFIUq9SIzSqCv7O1sUMiIiIieuhVOSnw8fEBAGg0mnoLhkgiEdDKzQYXE3IRmVLApICIiIioAVQpKdi+fTuGDx8OmUyG7du3V7rv6NGj6yQwarrauGqTgqjUfDza3t3Y4RARERE99KqUFIwdOxapqalwcXHB2LFjK9xPEASo1eq6io2aqDbu2sHG1zjYmIiIiKhBVCkpuLvLELsPUX1rzRmIiIiIiBpUtdcpIKpvZTMQxWfLUagoNXI0RERERA+/aicFr732GlauXGmwffXq1Zg9e3ZdxERNnIOVKVxszAAA/T4/iIHLDmHzuURoNKKRIyMiIiJ6OFU7Kdi0aRN69+5tsL1Xr17YuHFjnQRFVDbrUFaRErcyijDnr4v4bE+kkaMiIiIiejhVOynIysqCnZ2dwXZbW1tkZmbWSVBEHbyb6b5+tkdzAMDOSylGioaIiIjo4VbtpCAgIAB79uwx2L579260aNGiToIimtbbFy/2a4H9cx7BvGFtAABJucXIlSuNHBkRERHRw6fKi5eVmTNnDmbOnImMjAwMHDgQAHDgwAEsW7YMK1asqOv4qIlytTXH/OFtda+bO1giPluOq8n56BXgZMTIiIiIiB4+1U4KnnvuOSgUCnz88cf48MMPAQC+vr749ttvMXny5DoPkAgAAt1tEZ8tx5XkfCTmFMPVzhz9WjkbOywiIiKih0K1kwIAePnll/Hyyy8jIyMDFhYWsLa2ruu4iPS087DFniupWHcyDnFZcsikAnbO6osWjubGDo2IiIjogVfjdQoyMjIQFRWFixcvcoAx1bt2ntq1C+Ky5AAAlVrEvE2XoOY0pURERES1Vu2koKioCM899xzc3d3xyCOPoG/fvnB3d8f06dMhl8vrI0YiBLrrz3hlaSrFxYRcbD6fZKSIiIiIiB4e1U4K5syZg8OHD2PHjh3Izc1Fbm4utm3bhsOHD2Pu3Ln1ESMRXG3N4GhlCgDo5ueAGX21M12duJVT4TEqtaZBYiMiIiJ60NVo8bKffvoJw4cPh62tLWxtbTFixAj88MMP1V687MiRIxg1ahQ8PDwgCAK2bt1a4b4vvvgiBEEwmOFIoVBg1qxZcHJygpWVFUaPHo3ExMTqvi1q5ARBQE9/RwDA9D5+aO+lbTmISisod//fT8Sh9fu7cSgqvcFiJCIiInpQVTspkMvlcHV1Ndju4uJS7e5DRUVF6NChA1avXl3pflu3bsXJkyfh4eFhUDZ79mxs2bIFGzZsQHh4OAoLCzFy5Eio1epqxUKN38ePBWPHzD4Y2s4Nbd21YwxuZhShtJwGgYOR6dCIwIZTCQ0cJREREdGDp9pJQc+ePbFo0SKUlJTothUXF2PJkiXo2bNntc41fPhwfPTRR3j88ccr3CcpKQkzZ87E//3f/0Emk+mV5eXl4aeffsKyZcswePBgdOrUCevWrUNERAT2799fvTdGjZ6dhQzBt1sI3O3MYWtuglKNiLRiw30TsrUJanh0Jq6nFWDyz6dwLJoD4omIiIjKU+0pSb/66isMGzYMXl5e6NChAwRBwIULF2Bubo69e/fWaXAajQaTJk3CW2+9hXbt2hmUnz17FiqVCqGhobptHh4eCAoKwrFjxzB06NByz6tQKKBQKHSv8/PzAQAqlQoqlapO30NVlF3TGNd+kLV2s8Hp2BwkyQW9uhNFEYk52qSgUFGK0OVHAAC3MgpxcE5fo8TaWPHeqznWXc2x7mqH9VdzrLvaYf3VnLHqrjrXq3ZSEBQUhBs3bmDdunWIjIyEKIqYMGECnnnmGVhYWFT3dJX67LPPYGJigtdee63c8tTUVJiamsLe3l5vu6urK1JTUys87yeffIIlS5YYbN+3bx8sLS1rF3QthIWFGe3aDyKLEgkACZKLBL26y1cCxSrDWzstT45//vmnASN8cPDeqznWXc2x7mqH9VdzrLvaYf3VXEPXXXW69tdo8TILCwvMmDGjJodW2dmzZ/HVV1/h3LlzEAShWseKoljpMfPnz8ecOXN0r/Pz8+Ht7Y3Q0FDY2trWOOaaUqlUCAsLw5AhQwy6SFHFCs8k4si2q0iSQ6/uzifkAmdPGewvMzHB8OGh1b6fHma892qOdVdzrLvaYf3VHOuudlh/NWesuivrDVMVVUoKtm/fXuUTjh49usr7Vubo0aNIT09H8+bNddvUajXmzp2LFStWIDY2Fm5ublAqlcjJydFrLUhPT0evXr0qPLeZmRnMzMwMtstkMqPe5Ma+/oOmnZf2e55UJOBiciG6t3CGRCIgJV8JAGjjZoPYrCKUqLQjkeVKNfKVIpysTY0Wc2PFe6/mWHc1x7qrHdZfzbHuaof1V3MNXXfVuVaVkoKxY8dW6WSCINTZrD+TJk3C4MGD9bYNHToUkyZNwrRp0wAAISEhkMlkCAsLw7hx4wAAKSkpuHz5Mj7//PM6iYMar9auNpAIQFGpgKd/PI1h7dzw7bOdkZijHXkc6GGLz55oD40o4pX/O4eUvBIkZMvhZG2YEBIRERE1ZVVKCjSa+lkEqrCwENHR0brXMTExuHDhAhwcHNC8eXM4Ojrq7S+TyeDm5obWrVsDAOzs7DB9+nTMnTsXjo6OcHBwwJtvvong4GCDhIIePhamUrwzrDX+CI9EolyCPVdS8ffZRN0gY297S3Twbqb92sESKXkliM+Wo1Nz+0rOSkRERNT01GhMQZmSkhKYm5vX+PgzZ85gwIAButdl/fynTJmCtWvXVukcy5cvh4mJCcaNG4fi4mIMGjQIa9euhVQqrXFc9OCY1ssHrrlXkGDdCl+E3cCHO67CzU57T3rZ3xn43tzBEqdisnVTlRIRERHRHdVOCtRqNZYuXYo1a9YgLS0N169fR4sWLbBgwQL4+vpi+vTpVT5X//79IYpilfePjY012GZubo5Vq1Zh1apVVT4PPXye7+OLsMgMXEzIRUF6IQBt60AZb3vt1wnZ5SxqQERERNTEVXvxso8//hhr167F559/DlPTOwM2g4OD8eOPP9ZpcERVJZUIeGdYG71tdycFzR21rQbxbCkgIiIiMlDtpOC3337D999/j2eeeUavi0779u0RGRlZp8ERVUdPf0f4ON5JBNxs73Rta347QUjIYVJAREREdK9qJwVJSUkICAgw2K7RaLjCHRndx2ODAQAdvJtBKrmzHkFZ96Hk3GKo1PUzcJ6IiIjoQVXtMQXt2rXD0aNH4ePjo7f977//RqdOneosMKKa6NPSCf+81tdgLQJnGzOYmUigKNUgObcYPo5WRoqQiIiIqPGpdlKwaNEiTJo0CUlJSdBoNNi8eTOioqLw22+/YefOnfURI1G1BHoYrkotCAL8na1xNSUfJ29lMykgIiIiuku1uw+NGjUKf/75J/755x8IgoCFCxfi2rVr2LFjB4YMGVIfMRLViZEd3AEAf59NMHIkRERERI1LjdYpGDp0KIYOHVrXsRDVqyc6e+GLvVE4HZuDmMwi+DmxtYCIiIgIqEFLwbRp03DgwIFqrS9A1Bi42prjkVbOAICNbC0gIiIi0ql2UpCVlYVHH30UXl5emDt3Ls6fP18fcRHViydDvAAAe6+kGTkSIiIiosaj2knB9u3bkZqaikWLFuHs2bPo0qULAgMDsXTp0nJXHCZqTEJ87AEAMZlFUJY2vqlJw29kotvH+3EwKt3YoRAREVETUu2kAACaNWuGF154AYcOHUJcXBymTZuG33//vdz1C4gaEzdbc9iYmUCtERGTWWTscAz838k4pBco8HN4jLFDISIioiakRklBGZVKhTNnzuDkyZOIjY2Fq6trXcVFVC8EQUCAqzUA4EZ6gZGj0SeKIk7HZgMATt7KhlxZauSIiIiIqKmoUVJw8OBBzJgxA66urpgyZQpsbGywY8cOJCRw8CY1fq1cbAAA19MKjRyJvtgsOTILlQAApVqDY9FZRo6IiIiImopqT0nq5eWFrKwsDB06FN999x1GjRoFc3Pz+oiNqF60vN1SEN3IWgpOx2TrvT4YlY7BgWx9IyIiovpX7aRg4cKFeOqpp2Bvb18f8RDVu5aujbOl4NTtrkNt3W1xLSUfh6IyIIoiBEEwcmRERET0sKt296EXXniBCQE90FrdbimIbWQzEJ25nRTMGhgAUxMJknKLG+VgaCIiInr41GqgMdGDqGwGolKNiNgs7UN3fonKqAvyxWUVITZLDkEAegc4oZ2HLQDgUmKe0WIiIiKipoNJATU5d89AdC0lH1vPJ6H94n1YdzLeaDGtOXwLAPBIS2fYWcjQwasZACYFRERE1DCYFFCTFNJc2wVu49lEfHXgBgDg+M1Mo8SSmleCTWcTAQCvDtCu9RHsaQcAiEjKNUpMRERE1LQwKaAmaXJPX0gE4OiNTF2//aScYqPE8st/MVCqNejqa49ufg4AgPZe2qTgclI+1BrjdWsiIiKipoFJATVJzR0tMbSdm962pFzjJAUnbmnXI3i2h49uWwtna1iaSlGsUiM6veJZkhKy5dAwaSAiIqJaYlJATdbzfVvovc4sVKJEpW7QGERRxK3bLRVt3Gx126USAUG3uxBdSswt99hDUeno+/lBzPzjnFEHSRMREdGDj0kBNVkhPvb45PFgfDWhI6xMpQCA5NutBVeS87DywA0UK+s3ScgqUqKgpBSCAPg4WuqVtdeNKyh/sPHRG9oxEP9EpOLv22MSiIiIiGqCSQE1aU93a44xHT3h0cwCAJCcWwJRFPHGnxfwZdh13SDk+lI2nsHDzgLmMqleWfDtcQVXkvPLPfZayp3tS7ZfQUK2vJ6iJCIioocdkwIiAJ722qQgKVeO8wm5utWOf/kvRtd6UB9iMrRJQQtnK4OyVrqVlwt03YNupBVgzp8XkJRbjKu3kwIvewsUKdWY89cFDkomIiKiGmFSQAToWgqScorx56kE3XZFqQYr9l+vt+uWjSdo4WSYFLRwtoJEAApKSpFeoAAALNt3HZvPJ2H+5gjkylWQSgSsndYN1mYmOB2bg++P3Kq3WImIiOjhxaSACIDn7aTgelohdlxKBgC8NbQ1AGD7xeR6m+EnJlPbIuFXTlJgZiKFr6PV7bgKUKrW4L/baykcuZ4BAPB3tkKAizUWjgoEAHx9MBoFJap6iZWIiIgeXkwKiHAnKdh3NRVypRp+TlZ44ZEWkEoElKg0yChU1Nm1RFHE7A3nMXT5EUTcXrHYz9m63H1b3l55+UZaIS4m5qGgpFSvPNBdO2PRUyFe8He2QqGiVLcQGhEREVFVMSkgwp0xBWUNAs/28IFMKoFHM3MAQHwdDuL9/UQctl5IRlRaAZLzSgCU330IAFq6aMcV3EgvwNEbGQblbW8nBYIgYGovXwDAr8fjuHYBERERVQuTAiLcGVMAAFamUjzVxQsA0NxBO01ofFbdJAW3Mgqx9J9rettMTSR617/b3S0FZVOQPtLKWVdelhQAwOOdvWBjboKYzCIcLieBuFeJSo1dEalQNOzSDERERNQIMSkgAuBqYwapRAAAPNXFG7bmMgB3JQV11FLw+Z4olKg06BPghHG3Ew9fR0vdte9V1lJwJi4H5+NzAADvP9oW1mYmMDOR6BY4AwArMxOM7uAB4M6Yg8os3n4Fs/+6hD9u8tcAERFRU2di7ACIGgMTqQQhPva4lpyPab19ddu9bycFdbEGwJXkPOy5kgpBABaNCoSzjRk0IjAk0LXCY+6eqlQjAsGedmjlaoM/X+wBRakGDlamevt383PA/52Mx7m4nHLPl1OkxJm4HFiaSvHnGe0sS+ezJDh+KwuPtHar9XskIiKiBxOTAqLbfnuuG+RKtd6Ddl21FIiiiOVh2oXQRrb3QMvbaxB88VSHSo8zl0lhaiKBslQDAPh6YmcAQDsPu3L379zcHoB2wbMSldpgQbTFO65g24Vk3WtrMxMUKkrxwc5I7AlwgYmUrQZERERNEZ8AiG4zl0kNPnmvi6SgWKnGG39ewP5raRAE4PVBAdU6ft7Q1mjlao0dM/uguaNlpft62VvA2cYMpRoRl27PbHS34zezdF9bm5ngrxe6wUIqIjqjCBFJhvsTERFR08CWAqJKlCUF6QWKcj95r4ovw6Kw9UIypBIBS0a3Q8DtcQJV9XzfFni+b4sq7SsIAkKa22PPlVSER2ciNqsIA9u4wMnaDGn5JUgvUEAiAL8+1w0ezSzQvJkZfG1EXMsVcDkpD51utzQQERFR08KWAqJK2FnIYGOmzZ0Tc2rWWnAqJhsA8PHYIDzbw6fOYqtIZ59mAICVB25g3sZL+N+eKADAxYRcAEArVxv0bekM/9trI3jfHrbAlgIiIqKmi0kBUSUEQdANNq5JFyKNRsSNdO2qxV18Heo0top0vufT/pMx2i5DZd2Jgj31xyN4WWnXNIhIym+A6IiIiKgxYlJAdB+1WasgOa8YcqUaMqkAn/uMB6grQZ52cLYxg625toUjNkuOrEIFLt1uCWjv3Uxvf29rbVJwI60AJSouWkBERNQUMSkgug+/29OCXkmu/ifpZa0ELZysIWugmX3MZVKEvfEIjs4biAAXbReh8/G5uJSYCwDo4KXfUmBvCthbylCqERGZWtAgMRIREVHjwqSA6D56+zsBAA5dz4Aoijgdm428YlWVjo1O0yYFAbdXJm4ozSxNYWcpQ+fmzQAA2y4mI1eugkwqoLWb/kBnQQCCPLQrI5c3rmB3RAp+PxEHURTrPW4iIiIyDiYFRPfR1c8eVqZSZBQosGj7FTy15jje33q5SsdeT9N+8t7SpWGTgjJlswntuKhdmyDY0w5mJoYzKJUlBeuOx+HbQzehUmvXRcgrVmHWH+exYOtlbL+YjDy5CpeT8pggEBERPWSYFBDdh5mJFL0DtK0Fvx2PAwAcikqHWqP/YPxvZBp2XkrW21bWfaiVa/WmIa0r9w46njesTbn7dfXV7heVVoDP9kTq3ud/0Zkovf0+F22/goHLDmHkqnDM+O0MUvNK6jFyIiIiakhGTQqOHDmCUaNGwcPDA4IgYOvWrboylUqFt99+G8HBwbCysoKHhwcmT56M5GT9hy6FQoFZs2bByckJVlZWGD16NBITExv4ndDDbkAbF73XBSWliLqr/31moQIv/HYWM9efR/iNTPx9JgFv/X0RF25PA2qsloKWLta6KVWn9vJFjxaO5e7XJ8ARv0/vhqe7NQcA/HT0FlRqDQ5Fpev2yZWrkFWkBADsv5aOV9efq+foiYiIqKEYNSkoKipChw4dsHr1aoMyuVyOc+fOYcGCBTh37hw2b96M69evY/To0Xr7zZ49G1u2bMGGDRsQHh6OwsJCjBw5Emo1Z1GhutO/tbPuazMT7Y9N2VSfABB2NU33ifqsP87hrY2X8PfZO8mpj6NVA0WqTyIRsHBUIJ7u5o15w1pXuJ8gCOjb0hmLRgXCydoMyXkl2H4hGYevZwAA3h3RBsGednixXwtsfqUXAOBcfA4KFaUN8j6IiIiofhl1RePhw4dj+PDh5ZbZ2dkhLCxMb9uqVavQrVs3xMfHo3nz5sjLy8NPP/2E33//HYMHDwYArFu3Dt7e3ti/fz+GDh1a7++BmgZ3OwtM7+OHxBw5WrvZYuWBGzgVk41pvf0AAHsup+r2zZFrByHbW8qQI1chyNMWpibGy7+f6uKNp7p4V2lfc5kU03r74n97o/DhrqvIlatgIZNick9fvPCIv24/N1tzpOaX4FpKPrr6OuBqcj5eWncWc0NbYUxHz/p6K0RERFRPjJoUVFdeXh4EQUCzZs0AAGfPnoVKpUJoaKhuHw8PDwQFBeHYsWMVJgUKhQIKhUL3Oj9fO9WkSqWCSlW1WWXqUtk1jXHtB11D1t07Q1sCAM7G5WAltC0FSqUSBSWlOHYzEwAwb2hLfH3wFsZ0dMeCEW2wPzIDrV2tG+33trz6e7qLB/48HY/47GIAQHc/e0ihgUql0e3TzsMGqfkluBCfjY6eNth0Nh7x2XIsD7uO4YHOEAShYd+IEfDntuZYd7XD+qs51l3tsP5qzlh1V53rCWIjmUZEEARs2bIFY8eOLbe8pKQEffr0QZs2bbBu3ToAwPr16zFt2jS9B3wACA0NhZ+fH7777rtyz7V48WIsWbLEYPv69ethadkwC0zRg6tUA7xzSgqVKODVQDXSi4G/Y6RwtRDxbkc1SjWAERsG6kRxKbA1ToKzGQImtdSgg6P+r4k9CQJ2J0rR1VmDZwM0+PaqBJF52jc9rZUa/yZL4GMtYqyvBtKHPz8gIiJqlORyOSZOnIi8vDzY2tpWuu8D0VKgUqkwYcIEaDQafPPNN/fdXxTFSj+pnD9/PubMmaN7nZ+fD29vb4SGht63wuqDSqVCWFgYhgwZAplM1uDXf5AZq+725F9A2LV0rIk00c1C9FR3f4wYFNBgMdSFyurvCQBqjQipxPBnyTwqA7vXnUeuYIMRI3rjw4hDALSDkNfdNIFKLSKuUICNkwe+eDIIJrVcuK1EpcalpDyENLcvNx5j4M9tzbHuaof1V3Osu9ph/dWcsequrDdMVTT6pEClUmHcuHGIiYnBv//+q/fQ7ubmBqVSiZycHNjb35l6MT09Hb169arwnGZmZjAzMzPYLpPJjHqTG/v6D7KGrrsvnuqI+Vsu4Z+IVAgCML6LN2YOagWZzHANgAdBRfVXUY12au4AALiZUYTUAhUyC5W6MpVahKlUAhEidl1OxcC2rngixKtW8f0vLBrfH7mFMR09sHxcR0gkAuKz5LiVWYj+rV3uf4J6xJ/bmmPd1Q7rr+ZYd7XD+qu5hq676lyrUXdyKEsIbty4gf3798PRUX86xZCQEMhkMr0BySkpKbh8+XKlSQFRbdlZyvD1xM5YN7079s5+BJ8+0R7mD2hCUBMutuZwtjGDRgS2nE8CAHjZW8DOQvvLZ9bAAMzo2wKAdq2D2jpwLQ0AsO1CMj7bEwlFqRpP/3ACU385jW0Xkmp9fiIioqbOqC0FhYWFiI6O1r2OiYnBhQsX4ODgAA8PDzz55JM4d+4cdu7cCbVajdRU7QwvDg4OMDU1hZ2dHaZPn465c+fC0dERDg4OePPNNxEcHKybjYiovgiCgD4tnYwdhtEEe9rh38h0bDgVDwBo72WHcV28EZGYhxf7+ePErSx8c+gmTsdl1+o66QUluJlRpHv93ZFbuJlRhKRc7UDoD3deQ//WLrqEhIiIiKrPqC0FZ86cQadOndCpUycAwJw5c9CpUycsXLgQiYmJ2L59OxITE9GxY0e4u7vr/h07dkx3juXLl2Ps2LEYN24cevfuDUtLS+zYsQNSadP51JbIGIa1cwMAJN9e2bitmy36t3bBrEEtYWoiQWcfe0gEICG7uFarH5+4pU0qAt1t8VI/7bSo+2+3HJiZSJBZqMDysOu1eStERERNnlGTgv79+0MURYN/a9euha+vb7lloiiif//+unOYm5tj1apVyMrKglwux44dO+DtXbU52Ymo5h7v7IkWTncWZWvjrj9I39rMBIEe2m2nY2veWnDilnaRuJ7+jpgzpBXae9kBALwdLLDm2RAAwJ+nEyBXciE1IiKimmrUYwqIqPEykUrw5tA7qyS3cbMx2Kerr3ZAcl0kBT1aOMLURIKvJ3bG6A4e+OLJDujf2hk+jpYoVqkRdjWtxtcgIiJq6pgUEFGNDQ9yw+SePpjW2xde9hYG5WVJwbYLyZj4wwmsOxEHlVpjsF958uQqfLE3CrcyiiARgG5+2nN5O1hi5dOd0L2FIwRB0K2gvPU8BxwTERHVVKOfkpSIGi9BEPDBmKAKy7v5OcBUKkFesQrHbmbh2M0s/HosFr9P7w43O/MKj9NoREz++SQuJuYBAEa296hwIPHoDh5YeeAGjtzIRGahAk7WhtMNExERUeXYUkBE9cbJ2gx/vNAdnz0RjHdHtIGjlSlupBdi6i+ncCEhF9HpBeUet/FcIi4m5sHGzARrnu2M5eM7VniNABdrBHnaQq0RMeTLw/j+yE298stJeciTN+yy8kRERA8aJgVEVK9CfBwwvmtzvPCIP7a+2hvONmaITC3A2K//w+Avj2DvlVS9/ROy5fjf3igAwKxBARgW5H7fVYyXjG4Hz2YWyJGrsPSfSPx9JgEAcPh6BkauCscr68/Wz5sjIiJ6SDApIKIG4+1gibXTuqKdh62uO9CnuyOhUmsgiiIWbruMR/53EBkFCvg4WmJKL98qnTfExwFH5g3AzAEBAID3t17GtZR8/BQeAwD4LzoLNzMKax1/6e04iYiIHjZMCoioQbXzsMOu1/riv3cGwtHKFDGZRfjrTAJ2RaTgt+NxEEWgb0snfD+pC8xMqr7eiFQiYM6QVujf2hmKUg2e//UMjlzP0JVvPJuIQkUpFKXqGsWdmleCbksPYPz3J5CeX/N1F4iIiBojJgVEZBTWZiaYNVD7yf6HO6/i/a2XAQCvD2qJ36d3R+typji9H4lEwPJxHeFhZ65b8djRyhQAsO5EHLp+tB9jvz5Wo0/7d1xMRnaREqdisjF69X+Iy5IDABQqNVsPiIjogcekgIiMZmJ3H/Rr5YwSlQa5chX8nKzwcn//Wp3T3soUq5/pDJlUOw5h6ePBsLeUoaCkFMUqNa6l5ONWZlG1z1u2DoK5TILU/BIs3x+N85kCgj88gG5LD2D+5ggUK2vWCkFERGRsnJKUiIzG1ESCtdO6YuPZROyKSMGcIa1gLqt6l6GKdG5uj5+mdEVcthyhga7ILmqDn8NjIFeqkZRbjGM3s+DvbF3l82UXKXEmTrsA29cTO2P6r2ew+0oqLKQSiCKQUaDAH6fiUagoxcoJHSEIlQ+MJiIiamyYFBCRUQmCgKe6eOOpLt51et5HWjnrvn66W3M83a05Vh24gWVh13H8ZibMpBIk5hbjtYEBMJGW32gam1mEL8OuQy2K0IhAOw9bDGrrioFtXPBvZDqKSgX4OVrizaFt8PqG89hxMRmB7ra1bu0gIiJqaEwKiKjJ6BXgiGVhwMHIDOy+nApRBEpUarw7oq3BvnFZRZjw/Qmk3jWoeEigKwDg1QH++DcyHQCwYGQbDGzrjtxiJd7bchmr/r2BCV29YX97LAMREdGDgGMKiKjJaO/VDJamUhSr1CgbG/z9kVvYcj5Rbz+5shSTfjqF1PwS+DpawsPOHNZmJhjb0ROAdgrUBY+2wZN+avQNcAIATOzWHO08bCFXqvHLsdgqxSOKIgpKuLAaEREZH5MCImoyZFIJuvk5AABszEwwqYcPAODtTRG4lJir2++rAzcQny2HZzML/PVSTxx9eyDOvD8Yvk5Wun0m92iOvm53Zh0SBAGv3l4nYe1/Mfd92D9xKwuPf3sMwYv3YdPZxEr3JSIiqm9MCoioSRnfxRtmJhIsHBWIJaPbYXBbFyhLNXjht7PILFTgeloBfjqqXfTsgzHt4GJjDqlEqNIA6GHt3ODvbIX8klK88n/ncDEhF18fjMaCrZex+t8bkCtLAQA/Hr2FCd+fwPn4XADAigPXodZwWlMiIjIejikgoiZleLA7hrZzg0SinSFo+fiOeOybY4hOL8SCrZeRmFOMUo2I0EBXDGrrWq1zSyQCPn2iPSb/dApHb2Ti6I1MvfK/zybC2doMZ+JyAABPhnhh/7U0JGQXI+xqKoYFudfNmyQiasTS09OhUCiMHUaD0mg08Pb2RnJyMiSSuv1M3szMDC4uLrU+D5MCImpyyhICALAxl2HF+I4Y8/V/2H05FQDQzFKGD8YE1ejcXX0d8Otz3fDc2tNQlmrQv7Uz/F2ssfV8EuKy5IjLkkMQgHeGtcELj7TAsn3XsfpgNL45dBMdvJvB3c6iytdSlKqRkC1HgEv1F3prKKIo4vjNLAR62KKZpXbw9cXEPPxftAT/boxAF18HTOrpa9wgiajB5OfnQxAEeHvX7YxzjZ1Go4GdnR1sbW3rPCnIyMhAfn4+bG1ta3UeJgVE1OQFedrhhUda4NtDNwEAnz/RHm525jU+Xzc/B/z39kAIEsDWXAYAeKmfPzaeTYSVqRQ9/R3h46gdnzC5pw++P3ILlxLz0OvTfzFncCvMGtSySteZt/EStl1IxhuDW+H1wVU7pqFtPJuItzZewiOtnPHbc93w95kEvLslAiq1BMhIwbaLKQjxcUCgR+3+mBHRgyEvLw9eXl7GDuOh4uTkhMTERCYFRER14fVBLZFTpESAizVC27nV+nx2ljL91xYyTO/jZ7Cfi605fp7aFSv/vYFTMdlYFnYdHs0s8ERI+X80T8dm43JSHgLdbbHtQjIAYPn+63BvZo5xdbzWQ22pNaIu0TpyPQO/H4/Fgm1XAABB9hqY2TjgbHwu/jqTgMWj2xkzVCJqQFzgsW7VVX1yoDEREQBzmRSfPtEez/dt0eDX7tPSCX+92BOvDtAuevb2pkuYvzkCKXnFevtdTsrDMz+exJIdVzHxx5MAAPfbLRoLt11GoaK0YQO/j7CrabiVWaR7XZYQPN7JA9Nba/BKf21dbzmfhBKVWrffrYxCrDsRh2KlGkRE1DCYFBARNRJzh7TG2I4eKNWI+ONUPKb+fBri7QUV8uQqvPx/Z6Es1QDQfgpvaiLBxpd7wc/JCiUqDQ7eXlDNWIqVaoz5+j88/+tpKErV+OZQNACgRwsH3T52FjK8M6wVJALQ298R7nbmyCtWIexqGkRRxP+djMPwr47i/a2X8d6WCGO9lTqn1ogQRREqtQaz/jiPGb+dQa5caeywiIh0mBQQETUSEomA5eM74s8XesDSVIqotAKcuz1t6fdHbyIhuxjeDhbYOasPHuvkif892R6ezSwwLEjb3WnP7YHSxrLvaiouJuRi/7V0jFn9Hy4l5sHKVIqVT3dCGzftYOi5oa1gf3vAsVQi4Mnb3aT+tzcKXx24gfe2XIbiduKz+XyS0d9TbR2/mYVpv5xC24V7MOH7E1j1bzR2XExG2NU0TPj+BMasDsfALw4ZtAoRUdMVGxsLQRBw4cKFBr0ukwIiokZEEAR0b+GIobfHNWw5nwiVWoO/zmgXOHtnWFsEedph+fiOGHN7heXht5OCg1Hpet1wfj0Wi2ErjuB0bHaDxF42xgEAIlMLAAAfPRYEFxtz/DilC9Y821m3YFyZ6X384O1ggfhsOVbsvwFAO77jpX7arlTvbYlArlyJuX9dxKBlhxCRmNcg76Uu7LuSisk/n8TBqAwoSzU4GZONlQe079FcJkFkagEuJubhVmYRvtx33cjRElF5BEGo9N/UqVONHWKdYVJARNQIPdZJ+8C/81IK9lxORUaBAk7WphgSaLh2QrCnHTybWUCuVOPw9QwAQJGiFF/sjUJkagGe/fEkDlxLq9d4s4uUOHL72n0CnAAAT3T2wmOdtC0BXvaWGBbkbjAgrpmlKX6Y3AWWptrF4Z7p3hyzB7fEG0NaoqWLNbKKlBj33XFsOpeImxlFePqHE3h/awQ+3nUVSbmN99P1PZdT8Mr/nYNKLWJ4kBvWPNsZ1mbauT16tHDA9pl9MDzITTf4fNO5RNxIKzBmyOW6mVGI1LwSY4dBZDQpKSm6fytWrICtra3etq+++kpvf5Wq8tXsGzMmBUREjVDvACe42JghV67Cu7f71j8Z4g1TE8Nf24Ig6LoQbb+o/bR+87lEFChKIQiAolSDmevPIz5LXm/x/hORglKNiHYetlg7rSs2vNADnz0RXKVj27jZ4q8Xe+LTx4OxZHQ7CIIAMxOpbq2I62mFAABXWzMUKkqx7kQ8fjgag6HLj2Dr+aR6e08VEUVRN9ajPLsjUvDq+vMo1YgY09EDq57uhGFB7vhjRg9M7+OHryZ0QitXG3z7bAgWjAxEaKArNCLwwc6rjWJl61K1BrGZRVi07TIGLTuMkauOIk9e/Qedy0l5GLr8CN7eeKlRvC+imnBzc9P9s7OzgyAIutclJSVo1qwZ/vrrL/Tv3x/m5uZYt24dsrKy8PTTT8PLywuWlpYIDg7GH3/8oXdejUaDzz77DAEBATAzM0Pz5s3x8ccflxuDRqPBjBkz0KpVK8TFxdXbe2VSQETUCEklAp693dWmoEQ7q9CErhVPOVrWshB2NQ25ciV+Pa79w/HeiLbo0cIBxSo13t50qdKH2ZoqUanxc3gMAGBMRw+YSCXo0cIRJtKq/4kJ8rTDhG7N9Y7p6e+IsR09AADtvezw79z+WDAyEDMHBCDExx6FilK8+ffFKrUYpOQV1zgpUmtEvLPpEiZ8fxzP/3oaXT/ej8CFezH551PYd0V/zENCthyz/7wAtUbE45088eW4jrr3FOxlhwUjA+Fqq78GxrxhrWFqIsHRG5n4YMeVevkeVdWx6Ex0W3oA/b84pLuHMguV+OZwdJXPkZRbjA2n4jHh+xOISivAn2cSsHi7cd8XNW5ffvklvLy84OXlhUOHDumVxcTE6MpmzZplcOzo0aN15fdau3atrmzz5s31FT7efvttvPbaa7h27RqGDh2KkpIShISEYOfOnbh8+TJeeOEFTJkyBWfOnNEdM3/+fHz22WdYsGABrl69ivXr18PV1bAlWKlUYty4cThz5gzCw8Ph4+NjsE9d4ToFRESN1KyBARjYxgXHbmaiuYMlfJ2sKty3nYct2rjZIDK1AK9tuIDo9EJYmUoxvqs3hgS6YuiKIzh+Kwur/o3Ga4NaQqXWQFaNh/bKLA+7jluZRXCxMcP4rs3r5JxlPnosGEGedhjVwQNWZia67jZqjYiJP5zAyZhs/BwegwUjAys8R55chUdXhqNIUYods/ogwNkaBYpS2FnIKjzmbn+dScCG0wkG249cz8CR6xl4NNgdnz4RDBtzGZbsuApFqQY9Wjjgf091gFRy//nDA1xssHxcR7y6/hx+PR6HpNxiLBgZqFvgrqGE38jE9F9PQ1GqgZmJBK3dbNCvlTNW/RuNX/6LxbPdfeDRzAKnYrIR5GkLm9sL85Wo1DgXl4Muvg7YfTkFc/66qGsZaONmg6i0Avx+Ig6t3Wx0iS7R3fLz85GUpG31UygUemVqtVpXlpOTY3BsRkaGrvxeRUVFujK5vP5aSmfPno3HH39cb9ubb76p+3rWrFnYvXs3tm3bhoEDB6KgoABfffUVVq9ejSlTpgAA/P390adPH71zFBYW4tFHH0VxcTEOHToEOzu7ensPAJMCIqJGSxAEBHnaIcjz/n8IBEE7k89Hu67p+vZP79sCNuYy2JjL8N6Itliw7Qq+DLuOvVdSEZlagCFtXfH5U+11qy7XxPn4HPxw9BYAYOljwVV+0K4qazOTcteOkEoEvDIgACdjTuGPU/GYNTAAzW7PanSv747cRHaRdvrPOX9dgKpURFx2EX6e2hW9/J10+yXnFuPErSy42ZkjMbsYvxyLRaC7rW6cxqQePmjhbIVAd1vYWsiw9UISfjwag10RKUjLL8Ggtq7Yfy0NJhIBH44JqlJCUObR9u7ILGyHD3dexf5r6TgTl4Pdr/eFu51FdaqrxnLlSsz84xwUpRoMbOOCb57pDHOZFKIo4nRsNk7cysbj3x6Dh505LibmIcjTFptf7o3cYiWeW3sal5Py0dG7Ga6nFUCtERHkaYtBbVzxcn9//HosFp/sjsRHu66ip78j/J2tG+Q90YPD1tYWnp7a1k4zMzO9MqlUqiuzt7c3ONbZ2VlXfi8rKytdmaWlZV2GrKdLly56r9VqNT799FP8+eefSEpKgkKhgEKh0L23a9euQaFQYNCgQZWet6wL0oEDB+o1/jJMCoiIHhJjOnrik92RUGtEhAa6YvaglrqyST19UaRU49PdkbiSnA8A2HMlFVFpBVgwsi0GtHbRGwSs1oj45J9ruJKcj6+e7ggXG3OD65Wo1Hhr4yVoRG33pcHlDIKuT4+0dEJbd1tcS8nHwm1XsGxcB13rh0YjQiIRkJRbjF/+iwUAyKQCLifl645/488L2P36I0jMkeN/e6Nw9EamwTWupWj393W0xIKRgXpjOtq622JYOzdM+fkUzsTl4Eyc9lPM6X390NLVptrvZ0ovX/QOcMTM9ecRmVqAOX9exLrnu1cruaipFftvIFeuQhs3G3z7bGeYmWgHfguCgE8fb4/pv57GzYwiZBRoP8W9nJSP1zecx8WEXCTfHoh8ISEXANDL3xG/T78T94y+LXD0RibCozMx588L2PxK7wZ5T/TgmDNnDubMmVNumZ+fHxITEys8dvv27RWWTZ06tUFmB7Ky0m/VW7ZsGZYvX44VK1YgODgYVlZWeP3116FUaj+csLCoWrI/YsQIrFu3DidOnMDAgQPrPO57MSkgInpIONuYYcGjbRGZWoCFowIhuefB66V+/vB1tERCdjFaOFthwdbLiMkswnNrz2B0Bw+sGN8RC7ZdRkJOMUwkAv69vRjaBzuuYvbglvg3Mh0j23sgNb8E607EIT5Ljuj0QjhZm2HRqIq779QXQRDw9rDWmP7rGWy/mIwcuRKLRrXD8rDr2HMlFXYWMuTIlRBFoKN3MzzbwwdvbbyI9l7NUFCiwq2MIoR8FIayru6CALT3tENmofYP9/iu3jgQmY6ryXlYNLpduYO8OzW3x+/Tu2Pa2tOQSQXMHNgSE7vVvAtVgIt2APKjK4/i+K0s/BwegxmP1O8q2+E3MvH7Ce34gYUjA3UJQRlfJyvseq0vvjl0ExkFJQj0sMOCrZex+/YaEr6Ollg4KhBL/4lEqVqDFeM76j30SyQCvniqA0KXH8bFxDxsOpuIcZWMjyF60B09ehRjxozBs88+C0A7UDg6OhoBAQEAgJYtW8LCwgIHDhzA888/X+F5Xn75ZQQFBWH06NHYtWsX+vXrV69xMykgInqITO3tV2n5sCB33dddfBzwzeFo/Bweg+0Xk6EoVWPvlTtTl5Y92O28lIJ9V9KgVGvwv71RUKn1B4x+NDaowq479a1/axf8MDkEr/7feRy9kYnBXx7WlZV1GWrjZoNPnwhGGzdbPNLSCU7WZriWmo9xa46jSKmGIACPdfTEG0NawdtBv4l+1sAAlKg0sDDVf1C+WwfvZjj2zkCYSiUGiVhN+DlZYeHIQLyzOQJfhl3H8GA3eNlXvevAzYxC2JiZwMXWsHUHANLyS5CYU4zYzCJsu5is624WGuiKXgFO5R5jLpNizpBWutexmUXYcj4JU3r64vm+frAyM8GA1i5Qa8RyB5i72ZnjtUEt8dGua/jfviiMaO+um6L1fkRRhFyphlUV9ycytoCAAGzatAnHjh2Dvb09vvzyS6SmpuqSAnNzc7z99tuYN28eTE1N0bt3b2RkZODKlSuYPn263rlmzZoFtVqNkSNHYvfu3QbjDuoSf8KIiJooO0sZ5g9vC1OpBKv+jdYlBKM6eKCwRIVnuvvgZEwWfjgaA6VaAw87c11XkSc6e6G9lx28HSwwsE3Ddhu618A2rtjyai+8sykCFxJy4WJjhpVPd4KtuQxO1qZ6D8dlX7fzsMOp9wajUFEKS1OpbtDsvQRBqDQhKGMuu/8+1TG+qzc2n0/CqZhsLNp2Bd9P7lKlLjd/n0nAvE2XIBUEjO7ogYUjA3UJW3aREl/si8KGU/G4e4ZQqUTA0928MW9YmyrHt2BkoMHgbkEQYCKtOMbJPX2x7kQcYrPk+PHoLcwe3KrCfcuk5Zdg5vpzuJiYhxXjO2JEsPt9jyEytgULFiAmJgZDhw6FpaUlXnjhBYwZMwZZWVl6+5iYmGDhwoVITk6Gu7s7XnrppXLPN3v2bGg0GowYMQJ79uxBr1696iVuJgVERE3cK/0DsOV8EhJzitHRu5le94/eAU4QRaCFszUmdPXGpaQ8mJlI0Nbd1shR62vjZotNL/fCiVtZCHS3hb3V/VsurMxMGu2nz4Ig4OOxQRix8igORKbjyTXH8Mnj2taOzEIF0ou1ffi/PhwDhUqDlU93wv5raXh3SwREESgVRWw+lwS5Qo01k0IQnV6IKT+f0k3f6mVvAUcrU/Rr7YLHOnnCr5KZreqKqYkEc0Jb47U/zmPdiXi80j+g3C5ZZfZfTcP8LRG6cQxv/HkBbnbm6NzccLApUUO4d4yCr69vuVPtOjg4YOvWrXrbNBoN8vPvjGmSSCR477338N577xkcX955Kxt3UVca529DIiJqMBamUqx6uhN+DI/BW6Gt9T6RtjCV4v27PhHu6N3MCBFWjVQioHcF3V8eRC1dbfC/Jzvg/a2XcT4+FyNXhqOnvyP+i86ERjQBLpzS7fvoyqNIv/3wPKWnD4YGuWHyT6ew50oqPtp5FZvOJSJHroKfkxU+e6I9uvk5GOU9DQ9yg4uNGdILFNh7JRWjOnhArizF1eR8hPjY6wa7v781AutOxAMAWrvawMXWDEdvZOKF385iz+y+cLI2q+wy9eZiQi5OxmRhWm+/OpvSl6ix4B1NRETo1NweX0/sXOlaCNTwxnbyxP45/RAa6IpSjYijNzKhEQFTiQipRMCoDh5wtTXTJQSv9PfH4tHt0MvfSTeV64/hMciRq9Deyw4bX+pptIQAAGRSCSbcHoi97kQcFKVqTPzhJJ5ccxx/nNKuBXEwMh3rTsRDIgAv9muBra/2xppnQ9DSxRqZhQrM23gJqXklUKk1DRp7Sl4xJv10Ekv/icSvx2Ib7LrKUg00XBGaGgBbCoiIiBoxNztzfD+5C/ZdScWxm1kY28ENcRfCMXRYKMzNTHEzoxCf7o7EkLauerP6vD6oJY7eyEBafglm9G2ByT19qzQ+or493c0bXx+MxsmYbIxZ/R8iUwsAAMv3X8ejwe5YsuMKAOD5vi0wf3hb3XErn+6EMV//h38j09HjkwPwbGaB9TO619kib/klKtiYmehNzQto1684HZuNP07FI//26uJrDt/ExO7NYWl65zFKrizVe10XknKLMWZ1OKQSAS8+4o+nuzUv93tYolLjQkKurmtV2NU07L+WhhKVGgtHBTbYeheNhSiKyJErYWlqUufjfR5mTAqIiIgeAKHt3BDazg0qlQpxF+7MDuXvbI0fJncx2N/CVIodM/tAEGDwoGtM7nYWeLW/P1b+G43I1AIIAmBvaYqMAgVCVxxGWr4CLjZmmDUwQO+4tu62WDK6HRZuu4xSjYik3GK88NtZvD+yLQpLSmFvZYpOzZsZTKlaEZVag/1X0xCfLUd4tHYdhSAPO7w1tDXisorQ3NEKTtameGrNcciVagCAhUwKe0sZkvNKsObwLTzX2xcrD0Qj7FoqErKL8XhnT3z2RPs661r01f7ruilyP9h5Fd8cisarAwIwtZev3vf0jT8vYPflVHjZax/+E3OKdWWnY3Pw3aQQhPg0nbEYGQUKpOaXwFQqQStXmzqZFawpYFJARET0kGqsD0NzQlujfxsX/HDkFga0doGJVMCcvy4iLV8Bc5kEnzweXO6MUE93a44JXb2Rlq/AqNXhiEorwKSf7oytaO1qg02v9DKY7jQxR473t15GKxcrtNIApWoNZq2/iP3X0vT2i0jKw+Sf75zPXCZBiUoDX0dLuNiaY1ovX8iVasz9+yJWHriBbw5Go/Surj2bzyUhT67CN3ctAFddOUVKfLo7Eo7Wpth4Vrto16sD/LHtQjISc4qxZMdVRKcX4oPbq2Yfu5mpWzOiLBlwsjbD4509ceR6BiJTCzD1l1PY/HIvWJub4MStLNxIK0Rbd1v0belU7emEsxXAD+ExsLcyR58AJ4NpfI1FpdagoEQFqUSi606nVGuQWaQod/FFMsSkgIiIiBpc5+b2+PbZEADaFbSvJOdDrRHxUj9/uNlV/BAnCALc7Mzx3aQQvL7hPEylEthZyHAjvRBRaQV4e9MlrH66E07GZOPtTZfQ0bsZzsXnICG7GIeiMuBiLsX6lDM4F58LUxMJRgS5oYWzNfq2dMKawzdx/GYWWrvZ4Hx8LkpUGrRwtsKWV3rDzkKmi/VmRiF+PRaLIqUaLV2sMW9YG5SqNZj95wUciEzHgq2X8dkT7WvUQrP0n2v4++ydFXwHt3XBW0PbYPbgVvj1WCw+/uca/u9kPNQaER+ODcJHO68BAMZ38UYbdxsIAMZ31XYzmj24Jab8fAqnY3Mw9uv/UHS7xaOMmYkE03r74dUB/npJmLJUozcz1Ln4HITfyESAkyW+jJCiQHUDgLblZMes3ghwqf4K3nWhVK1BjlyFEpUaecUqaO6asUcmlUCl1iA9X4GsQiUsZFI0d7SEpBG1mjU2TAqIiIjIqKQSwWDdg/vp3NweR+cN1L0+G5eD8d8dx65LKXCwNMWeK6nIKFAgLksOQDsNa7FSjfQiJdLjcyERgNVPd0JoOzfdOb6bdKcb1tXkfPwTkYKnuzfXJQRlsc4b1gYv9ffH5cQ8dPVz0HUXMjeVYvra0/jrTCI8mlngtYEtq9VaE5GYh43ntAlBkKctsgqVePv2+hEyqQTP920BV1tzvL7hPDacTsCJW1mIzZLDxtwE84a1huM9szJZmprgu0ld8Ng3/yEuSw5BADp4NUNrVxucjc9BdHoh1hy+ictJefh9ejcIgoBfj8Xig51X8URnTywa1Q4AMOPXM8i6vRggIKCFkxUkEgHR6YWY/ecFbH65d6XTy9ZWfrEKoijC1kKGUo0IlVoDmVSCWxlFUJTeSXTMZVKo1BoIAFo4WSE+W45ilRoatfaY5JxieNpbNKrudI0JkwIiIiJ64IX42GPx6HZ4f+tl/H4iDgAQ4GKNIA9bZBQq8PmTHWACDVb+fQA+rQLRvYUTOlQyxW6ghy0CPSpej8PWXGawAvSA1i5479FAfLjzKlbsv4EzsTn431PtKxzoe/cn8hqNiCU7rkAUgbEdPbBiQqdyjxnVwQMZBQp8sPMqYrPksDSV4qsJHQ0SgjIOVqb4+8WeOHojE70DnHStMKIoYv+1dLy6/hzCozNx+HoGgjzt8PmeSKg1Iv46k4gzsTnoFeCIrCIlbM1NoCjVwNNCjb9e6AY1JBi64gguJ+Vj4bbL+PixYIMF9kpUavwbmY6eLRyrtHbIvURRRGp+iW6tCguZFIpSDTSiCAECRIiQSSWwtzSFlZkU1mYmEAFA1Had83WyQkFJKURRRHJuMbLlSqhFEc7WZjA1kZS7+nZTxqSAiIiIHgrP9vCBtZkJ3tp4ERJBwOqJndDG7c6DvUqlQjcXESN6+UAmK38V69p6rrcvTE0k+HjXVYRHZ2Lo8iP49In2GBHsjly5Eufjc1GoKMXP/8XgclIepvT0xeuDW2LDqQScicuBpan0vqtLT+vti/wSFY5FZ2Hx6HaVJi+AdiXvJ0K89LYJgoAhga6Y0tMHPxyNwae7IxHobosipRr+zlaQK9W4lVmEW5lFAIAPxwYhtI0T9uzZAzsLGWQyGT59vD1e/r+z2HA6AQWKUiwf11EvyZm5/hz2X0uHi40ZVkzoiF7+VV9HRKMRkZAjR16xShdvsUrbKiARBGhEESYSCVo4WcHsrhmGBN1/tK0rDreTERHamaTyilW6c1qamsDFxgw25iYQRUCh1sDcRNJkWxKMmiIdOXIEo0aNgoeHBwRBMFj9TRRFLF68GB4eHrCwsED//v1x5coVvX0UCgVmzZoFJycnWFlZYfTo0UhMTAQ1Pmq1GufOnUN8fDyUSuX9DyBqIjSahp1vnehhNraTJw6+2R/75/TTSwgaiiAImNTDB7te64sOXnbILynFq+vPYcX+6xi47DCmrT2NWX+cx/n4XKjUIn4Mj0GXj/bj872RAIAFIwPh0azyKUQFQcDswa3w10s975sQ3M8r/QNgY26CyNQCbD6fBAD4cEwQtr3aG23ctGMFWrvaYFR7D5hIJbi7MWBYkBtWPd0JMqmAXZdSMP3X0/h0dyTGf3ccz/16GvuvpQMA0gsUmPzTKVxNzje4fnk0GhExmUXIK1ZBEAR421uilYs1nKzN4OtohUB3W/g6WSHAxVovIaiMk7UZWrrYwM5CBhOJ9vFXrixFbFYRrqcVIjK1ADfSCnA9rRD5t5OGqujfvz9mz56te+3r64sVK1ZU+fjGxKhJQVFRETp06IDVq1eXW/7555/jyy+/xOrVq3H69Gm4ublhyJAhKCgo0O0ze/ZsbNmyBRs2bEB4eDgKCwsxcuRIqNXqcs/ZmImiaPBwoNFoEBMTg7S0NBQWFhock56ejvz8fKSkpJR7To1Gg4yMDKhUVb/Ba0MURURFRWHlypWQy+V6ZZmZmQgJCYGPjw86dOhgcOyRI0ewdetWg+QQABITE5GYmAi5XG6w9LdKpcL+/ftx6dIlZGZmGhyrUqmg0WgM4gGAxYsXo1u3bvD398f169f1yuRyOU6fPl3uvZSSkoJff/0Vc+fOxQ8//FBuXVDNlJaW4urVqzh37hwiIyMNysPDw7Ft2zacOHECCoVCrywqKgrbt2/H2bNnq3XPx8fHY/78+Xj11VexatUqg/L169fj3XffRURERLXeS2FhIXbv3o3nnnsO3333nUF5165d4ePjgyeeeMKgbNu2bfjll1/w999/Izs7u8rXVCgU2Lt3Lw4dOlSt44geJl72lkafFcff2RobX+6FZ7o3hygCK/bfQHaREm625gjytMXzffzwzTOd4e9sBUWpBiq1iEFtXDDhrrUmGoK9lSk+e6I9Qnzs4edkham9fNErwAkutub488WeWDQqED9N7VLh2IiR7T3w05SusJBJcfRGJtYcvomTMdk4FJUBAPhwTDv0a+WMUo2Ij/+5WqWYMgoVKFKWQioR4OdoBXsrU5jJpPBoZgFbCxkkEgG25rJqj2OwMJXCx9EKgR62aOtuC2cbM0gFAYpSNUo12rEIilI1YrOKkFmo/fuiUmuQK1di0uQpEATB4N/nn3+ODz/8sMJrlvehd6MlNhIAxC1btuheazQa0c3NTfz0009120pKSkQ7OztxzZo1oiiKYm5uriiTycQNGzbo9klKShIlEom4Z8+eKl87Ly9PBCDm5eXV/o3UwDfffCO2aNFCNDMzE48cOaJXlp2dLULb6iU+++yzBseOGzdOBCC6ubkZlC1dulS0sLAQAYjr1q3TK8vJyRGDg4PFSZMmiZcuXTI4NjU1VTxz5ox45swZg7Lly5eLw4YNE5966ikxJiZGr2zevHm6eP/55x+9sitXrujKnn/+eYPztmrVSgQgtm3b1qBs9OjRumMPHz6s265UKsXPP/9cV3b3/VImICBANDU1Fd977z2DsgEDBogAREEQRLlcrle2bds23XnvvjdFURR37typK5s6dapeWUFBgdixY0exbdu24oQJEwyuOX/+fHHkyJHi+PHjxaioKL0ypVIpZmdnGxxTX5RKpbh161ZRqVTW+bkXLlwoDhkyROzQoYMYFxenV7Z161bR0tJStLCwEL/88ku9srS0NF3d9u7d2+C8jz32mK48Pj5er+zrr7/WlU2aNEmv7OzZs+LUqVPFp59+Wvzhhx/0yuLi4nTHhYaGGlzz8ccf15WnpaWJonin7r766isxJCRE7Nq1q7ht2za94+6+h5YsWWJwXhsbGxGA2KpVK4Oyvn376o49f/68XtnGjRvFtm3bikFBQeLff/+tV5aQkKA7zsXFRVSpVHrl//33nzhnzhyxQ4cOYlFRkcF169rBgwfFMWPGiMOGDROnTZsmajQaXd0pFArxl19+ERcvXix+++23Bsd+/PHHYr9+/cRFixaJGo1GrywyMlL85ptvxE8++USMiIio9/dRRq1Wi1FRUWJ0dHSDXfNe9flz+7AzRt2p1RrxjQ3nRZ+3d4pPfvufmFesf22NRiNeTc4T/z6TIBaWqCo4S+NQWf2di8sWB/zvoDjxh+Pib8djxUXbLou/HYsRRVEU47OKxJbv/iP6vL1TvHCt8p8dZalajEjMFS8m5Ig5RYr6eBt6VGq1mFlYIuYWKURVqVpMzJaLFxNyxIsJOeKVpFzd16OffFrsO2CweOBspO7fpesxYmlpqd75fHx8xOXLl+telz1DqNVqMScnR1Sr1TWK83737L1/D8tU5xm30Y4piImJQWpqKkJDQ3XbzMzM0K9fPxw7dgwvvvii7tPAu/fx8PBAUFAQjh07hqFDh5Z7boVCofcJY36+tjlLpVI12Cfqd0tPT8etW7cAaN93jx49dGV3f9KXn59vEF9Zd6q0tDQUFRXB1PTOQB6VSoXiYu2cxY6OjnrHJiYmIiIiAhEREejQoQPatNHvvzh48GBcvnwZgwcPxj///KNXdu7cOezZswcAsGDBAr3zdu7cWff17t27MXjwYN1rmUyGGTNmID09HaNGjTJ4L2Wx3rx5EyUlJZBK7zQJ+vr66r62sbHRHatSqfQ+4TcxMdE7r0qlQkxMDNRqNTZu3IhFixbpXTMtLQ2CIKBjx44Gx+7YsUMv9rvLgoKCdF97e3vrlZmYmODChQsAAFtbW4P3efToUYSHhwMAPvvsM73yvXv3YsyYMXBxccH//vc/jB8/XldWVFSE6OhotG3bVu/7XFVZWVlIS0tDYOCdGT5UKhVOnTqFq1evIiAgAKGhobC0vPPp2vnz5/HDDz8gOjoakyZNwqRJk/TO+f777+PUqVPo06cPFi5cqFf233//4cCBAwC0Xcfufp8KhULXclNSUqJX1qxZM5iamkKpVKK0tNSg/lJTU3Vf29vb65Wbmd0ZaDdy5Ei9sqysLKxduxYAYG5ujilTpujK3NzcYG9vj5ycHOTl5Rlc8+LFiwC0389mzZrp/a5ITU3F2bNnAQBKpVLv2ObNm+u+trCwMDivg4MDTE1N4ejoCIVCAYlEoldWFmurVq30jk1PT8e1a9ppCHNycvTK7m5RfOyxxyCKol75Y489hvT0dIwYMcLgvt6yZQuOHz+OgIAAvPDCC3qxfvvttzh79iyysrKwZcsWvbKwsDA8//zzcHBwwOeff44hQ4boykpKSrBt2zYAwPDhw/W+p6WlpZg1axYKCwvRvn17TJ8+Xe+8Fy5cwOHDh3H48GG88cYbevfm6tWrda3Mrq6uaN26ta5MFEV07twZ+fn5CAkJwV9//aV33lOnTqG0tBQ+Pj7w9PTUKxs9ejTOnj2L0tJSrF+/HoMGDdKV/fzzz3jnnXeQm5uL+fPnY8mSJXrHvvrqqzA3N0fLli3x0ksv6ZVdu3YNkZGRSEtLw4QJE9CsWTNd2d69e/H333/j1q1b+PLLL9GxY0dU5u7ff1Q9xqq7Tx8LxOQe3mjlag2Z1PD6AU4WCHCyACA26u9rZfUX5G6Nva/3LvcYNxsZpvRsjh/CY3E9rQBeXgoUlJRCo9FAIwKFilJoRMDW3ARFKjUUKjUsTKUwkQCFJfXT3dhCJoUgCJAAsL9rdil3OzNIJNoF0MrWoDC73SJhIjOFq5sbLGVSFChKIQLo138AQjp3wvLly3XnEG/3/GjRogUA7e9dQPu8EBMTA41Ggx07duCDDz7AlStX4OHhgcmTJ+Pdd9+FiYn20VwqleLrr7/Gnj17cODAAcydOxeLFy+u8P1oNJpyvy/VuZ8abVJQ9off1dVVb7urqyvi4uJ0+5iamsLe3t5gn7sfHO71ySefGPwyB4B9+/bp/dFpKDKZDIIgwNPTExEREbCzs9OVZWdno0+fPlAqlTAzMzN4QPfw8ACgfVjZunUrrK2tdWWZmZnw8PCAm5sbYmNj9Y69fv06TExMUFpair179yIg4M7KkRqNRvegferUKezatUtv0M2NGzd0X58+fVqX0ADaP/IdOnRAx44d0bp1a4N4H330UQDaH5h7y4YMGYLi4mK4ublh586deoPA7Ozs0KNHDxQVFeHSpUuIj4/Xlfn7+2P06NEoLi5GUVGR3nlzc3MREBCA7Oxs2NjYYPPmzTA3vzP/9ZIlSyAIAkxMTAziadasGXr06IGcnBxcv34dpaWlujJRFDF9+nR4eXnBx8fH4Fhra2toNBooFAqDsrLubx4eHrhw4YIugQC0D14ajQapqam4deuW3rGxsbGYPXs2TExM8Mgjj+C1117TO+/ff/8NKysr+Pj4oF27dnplb7/9NqKiogAAf/31l15ScfXqVV3T5scff6x37NmzZ/Hjjz8C0N5jjo6Oeuf9/fffkZKSgkuXLqFTp056iVzZQ62JiQnCw8Nha3un32tkZCR8fHwAaLti3VtHw4YNg1KphJubm0FZ79694efnB7lcrks6yigUCjz99NNITk6GIAh6xxYVFem+zs3NNTjvu+++C0EQYGNjU27ZyZMnERsbi927d+uVpaenQyKRQBRFZGZm6h2rUCgwfPhwdOjQodz75KuvvtJ9XZZol+natSs8PDwglUoRFhamV3b16lVYWFhAo9Hg2rVreufNz8/H+PHjkZubW+7PYNl4HgsLC+zYsUP3PVMoFHj55ZeRnZ2NgIAAeHnpD0r87bffdMnPxo0b9X5XhoWFISUlBSkpKdi9e7feHyG1Wg1HR0dkZWXBz89PL56wsDBYW1ujsLAQERER+Ouvv/R+h8XExOi+3rJli97veisrK736uPu8SUlJug9MPDw8DOpg9uzZiI2NRVBQED766CO9MpVKhYwMbbeHyMhIvQ+QYmJikJubC8DwHlKr1fjpp5+g0WjQtm1bvYQQ0H6AUtb9zMrKSu9n6bvvvtPdV5s2bUJycrKurLCwEAsXLoS1tTWmT5+u+7kpq7/IyEhYWVnBxsZGL9Ggyt37M9VQ4oxy1bpXk/oLUAO+1lLdatSAdnaicd+dqOvwquT4nB6wMC1/PIIFAA9LQBQBiQBIJRqYSwG5BHAxFyGTlELQAPkqQFGqQX6xEjm5+ZBKtM9QxcUlSM/Ox58796NHcEt8sOxrPDJgEDyspSgoKMCBAwcwbdo0fPbZZ+jZsydiYmIwe/ZsKBQKvP3227o4Fi9ejIULF+KDDz6ARCLRfYhdnqysLL3niTLldZ2uSKNNCsrcOwJcFMX7jgq/3z7z58/HnDlzdK/z8/Ph7e2N0NBQvQeXhtK/f3/4+PjgscceK3c2hGeffbbCY0eMGFFp2bJlyyose+WVV3DgwAEUFBTonSc3NxcjRoyAk5MT/P39ERoaqhdX2biOgoICeHl56T0IAsC4ceMqjKky93svCxYsMNhe9vDx2muvVTiTxMSJE+s8HuBOglOeyvpyd+vWDRqNBkql0uDB69KlS8jIyEBaWhomT56s9ynmyZMnAWgTr3bt2hnEN3HiRMjlcgQHB+se3sr88MMPuqSgR48ecHPTzsutUqlw6dIlXVJgY2Ojd96uXbvq+kpaW1vrlWk0GmRlZQHQ/sy1bNlSr8WpS5cuWL58OZydnQ1+HkeMGIH58+dXWEf3uxcqM2PGjArLWrVqBSsrK1hZWcHd3b3S89zr3lYSlUqFsLAwLFu2DF9//TUUCgXMzMz0Pu0H7nxCVF33q4Mvv/yywvIJEyZUWPbKK6/AxsYGkyZNgouLi277mjVrdPetv7+/wfXLkkMAaNu2rV7ymJycDHd3d+Tk5KBly5YGx545cwYWFhawtraGqampru6GDBmiG5DXoUMHtGjRQu9eGTFiBG7duoXTp0/j0Ucf1UsYunfvDmdnZ/j4+KBLly56Pyv//PMP/P39kZ+fj6eeesognnfeeQeA9gOOgQMH6n1QoFKpEB0dDQCYOnWqXvLRvn17/PrrrwgJCcFzzz2nNzYqKSlJNybMycnJ4Jpr167VJQVPPfWU3jWtrKx0SYGXl5fesefOndN98JKcnIyXX35ZV3/9+/fHyy+/jJSUFEybNs1g3Mrrr7+O7Oxs+Pn54YMPPtArKy3VfkpbUatjbm4ukpKS4O3tbZS/i/Xl7nuvvmYfUigUyMnJQUpKClq3bq2XQMfExGDjxo3w9PREUFAQ2rdvrysTRRHLli1DXl4eWrZsicmTJ+ud9+LFi7h06RLc3d3RqVMngw9pGkJt62/4UDVOXLkJQRBgbymD5q7VoBuaja0NLE2r/hhsbibDwbC98Gt+5+92v0HanioqDZChlMDX0RIQBBSWCkgvASyaaWdbcnN2QLd2LaCQF8HGxgZfffUV3nnnHbz44osAtL9bCgoK8M477+Djjz/WnX/ixIl45ZVXqhSfo6MjgoODDbZXlkgYqEZ3pnqFe/pt37x5UwQgnjt3Tm+/0aNHi5MnTxZFURQPHDggAjDog92+fXtx4cKFVb62sccUsH9ozTWlurt586b4zDPPiAEBAeLOnTsNyi0tLUUAYpcuXQzKVq1aJfbo0UOcOnWqrk+8KGrr7++//xbXrFkjLliwQPz3338Njj1+/LiYm5trsF2j0YgZGRlibm5ujftIPsgetnuvrK/8kSNHxNOnTxuUR0dHixEREWJ2drZB//7qasi6u7e/ryiK4ooVK8TXX39dHD9+vHjz5s0qn0uj0VT43ktLS8Vbt26J//33n3jx4kWD8t9//1388MMPxbVr15Z77L59+8TCwkKDsh07dohSqVQEIHbq1EkUxTv1t379et34kaefftrgWF9fXxGA6Ovra1D2119/iba2tmKbNm3E2NhYvbL9+/frzvv2228bHBsVFSUeOHBAPHjwoEHZt99+K77++uviO++8Y1Cm0WgMxrg0tLvvPY1GI+bk5IhFRUUGv8Oio6PFSZMmif369RPnzZtncJ5ffvlFfPnll8VPPvnEoOydd97R1d+JEyf0ys6ePasre+ONNwyOdXV1FQGIAQEBBmWLFy/WHbtjxw69soiICLF79+7itGnTxD///FOvTK1WixEREeLp06fLvd/Pnj0rpqamGmwvT3k/u2XjhO6m0WjEuXPnim+++aZBrPHx8WJRUZGYlZUl5uXliUUKld6/nAK5mJKRLebLSwzK6vJfdX+PTZkyRRw8eLB448YN3b/k5GSxT99HxEnPv6wbe+Dh5S2+tWipGJGYKyZmy8sdU2BpaSmam5uLVlZWun/m5uYiAN1YL5QzHrQyD/WYAj8/P7i5uSEsLAydOmkX8FAqlTh8+DA+++wzAEBISAhkMhnCwsJ0n06npKTg8uXL+Pzzz40WO1F9aNGiBdatWwcABjMwAdruFXFxceW2ks2cORMzZ84s97wymQzPPfdchZ/63D3G5W6CIMDJqepzTlPjJpFI0KpVK7Rq1arccn9//waOqG7c25IJaD9Br4nKWqClUin8/Pzg5+dXbnllLb5SqVRvHMbdRo4cieLiYqSmpuq17ADaMVzz5s3DrVu30L17d4Njy1ryyv5/tzVr1iA/Px/5+fkG7+vucSl3d1cCtC2EISEhKCwsxOOPP47+/fvrlf/f//0fwsPDYWdnh48++kiv/sPCwvDEE0/Az88P33zzDfr06aMri4+Px5YtW3Dr1i0sWbJEryvU9u3b8f333yM9PR0zZswwaA2cOHEiCgsL0bx5c4PZDCdPnozs7GyEhITgrbfe0ht39NFHH+nGQu3atcugdef3338HAL0uvWV+/PFH/Pfff7C3t9e1PJW5u2UlPj5e73tzd4tWQkKCwXm9vLyQlpaGmzdvQi6X67Uy3D3L4L0tnQUFBTh58iROnjwJQRD0WuxFUdR9guzv769rCSvz9ttv48CBA+jTpw++//57vRbfsr81arXa4D4pKCjA5MmT8e+//2LJkiV603IKgoA1a9agqKgIJ0+exMiRI/WOLRvjBmjv47tbWIsL8pAYq+066Ovra/B3pqSkBKampgatsg3ByspKr7s1oF3h2s5COxOSslQDQICthQxt3W0grSBGjUaDJUuW4PHHHzcou7cVsSEZNSkoLCzUuzljYmJw4cIFODg4oHnz5pg9ezaWLl2Kli1bomXLlli6dCksLS113UHs7Owwffp0zJ07F46OjnBwcMCbb76J4OBgvQGuRA+b8h5O7h5wT0QPD5lMBm9vw2kqW7RoofuQrDzx8fHIzMwsdxpnJycnuLq6Qi6X6z0oA9oEsUePHmjRogVCQkL0yqKjo3VJQ9mAyLvl5eXp/n/t2jXdpAyiKOL999/XjR8pGw9X5syZM7qHyv79++t1u9NoNNi1axcAoF+/fgbX3LZtG+Ryud4EEGWKioqwa9cu7Nq1C6+99pree727++a96xv5+vrCzMwMCoXCICmQy+U4deoUAO1A/4KCAtjY2OjK27Zti1GjRsHNzc3g++bs7Iy//voLCQkJ5SbaK1euRHFxMTQajcFD76RJkxAYGIiUlBS9yTeAO92mRVHUfZBaRiqVwsrKCkVFRQZjMAGgTZs22L9/P44ePar3PgDgwIEDePLJJ1FUVITTp0/rdRvMysrSdT29efOmwXnt7e1RVFSEM2fOQKVS6X3wdPfU8kqlUu9B+O6/b/feu2VjHlUqFdzd3Q3uo5KSEt34v7u7G9Y3qURAgLM1ipRqyKQCrM1MdAmBTCYzmNq8c+fOiIqKMkgwjM2oScGZM2cwYMAA3euyfv5TpkzB2rVrMW/ePBQXF+OVV15BTk4Ounfvjn379undtMuXL4eJiQnGjRuH4uJiDBo0CGvXri330yEiIqKmolmzZuUOPpbJZPjzzz8rPG7UqFEYNWpUuWVqtRrPPPMMnJycMGzYMIPydevWISsrC61bt9Z7YMvNzYW7uzt8fX0hiqJBi0pSUpLu67179+olBUOGDIGZmRmUSqXehAFlLCwsIJfLdTPY3e3u1pV7k5+2bdti0KBB0Gg0BmVSqRQXL16Ep6enwcO5paWlbv2gsrFEdxs7dizGjh1rEAugTbieeuqpcssAoFevXhWW9e7dG717G87uU3ZcWcJVXgL5wgsvQKFQlFsWGhqKvXv3Ii8vr9xkrSzRi4qK0ksKysYgOTs7l3ufbd26FUVFRSgqKjJYg8nT0xMFBQUQRdGgfi0sLODs7IyioiKDxDMrK0s3WUJ5awhdvXpV9/28t399Tk4OSktLq93KnZ6ejvT0dGRlZZXbSq/RaFBaWgpRo4bdXbMYaTQa5ObmwsvLC7t27ULPnj2hVCpha2uLhQsXYuTIkfD29sZTTz0FiUSCS5cuISIiwmDyg4Zk1KSgf//+5VZwGUEQsHjx4kqnYDI3N8eqVavKXXCIiIiI6k7btm113RjLc/fA2bvZ29vrpqbVaDQGrZ2hoaH4+eef4eDgYNAaYGVlhfj4eDg4OJTbOnHhwgWYmpqWO3vgN998g9deew0xMTG6GbvK9OjRA/v376/wvdw9ze29PD09DaazNTZLS8tyu5EBqHRiglGjRmHkyJHIyckx+L6UfSLv7Oxs8PDu4+ODkydPIiQkpNwPYu9tZbqbnZ1dud2yAG1ScG+3tTKWlpZo1qwZ5HK5QTxqtVr3/b03UQO0A/WLi4shkUgMkoK4uDjdtO73fnoviiJKSkogiqJBIlJaWoqioiJkZWUhMTFRL9kVBAGxsbGYOXMmVq5cCR8fH7i7uyM2NhZDhw7Fzp078cEHH+Dzzz+HTCZDmzZt8Pzzz1dQYw2j0Y4pICIioodPeX3BW7duXelD+L3jKe527yxudxMEAW3btkXbtm0BwOATa9ISBEE3jfTdFixYoDfz393TDTs6Ojb4DEjl9ekvI4oinJycIJFIKu06VN6H0Wq1GnK5HHK53KD1x8rKCoIg4LPPPtPN3FdGoVDoZv0qS6hiY2N15ZaWlnjkkUcwePBgBAUF6c0ENHTo0ArX06oozvrGpICIiIiIHmgmJiYGYy3u5u7uXu6AaQB6U/MWFhYaJAWdOnUqN5kVBEGXGJU3KNjd3R2iKDb4gOGaYlJARERERA+18lpCynh5ecHT07PcMQ6CIFQ485ilpWWFM44B+jNXPQitVEwKiIiIiKhJq+zhv6lo+EleiYiIiIioUWFSQERERETUxDEpICIiIqIGY4yZdR5mdVWfTAqIiIiIqEHY2dkhMzPT2GE8VDIzMytc96E6ONCYiIiIiBqEra0t0tPTkZCQYOxQGpRGo0FWVhYcHR3Lnd60NszMzGBra1vr8zApICIiIqIGU9lidA8rlUqFCxcuIDg4GDKZzNjhlIvdh4iIiIiImjgmBURERERETRyTAiIiIiKiJo5JARERERFRE8eBxrgzv2t+fr5Rrq9SqSCXy5Gfn99oB580Vqy72mH91RzrruZYd7XD+qs51l3tsP5qzlh1V/ZsW5W1DJgUACgoKAAAeHt7GzkSIiIiIqK6VVBQcN+1DASRy8pBo9EgOTkZNjY2EAShwa+fn58Pb29vJCQk1Mk8s00J6652WH81x7qrOdZd7bD+ao51Vzusv5ozVt2JooiCggJ4eHjcd30EthQAkEgk8PLyMnYYsLW15Q9ZDbHuaof1V3Osu5pj3dUO66/mWHe1w/qrOWPUXVVXO+ZAYyIiIiKiJo5JARERERFRE8ekoBEwMzPDokWLYGZmZuxQHjisu9ph/dUc667mWHe1w/qrOdZd7bD+au5BqDsONCYiIiIiauLYUkBERERE1MQxKSAiIiIiauKYFBARERERNXFMCoiIiIiImjgmBQ3gm2++gZ+fH8zNzRESEoKjR49Wuv/hw4cREhICc3NztGjRAmvWrGmgSBuXTz75BF27doWNjQ1cXFwwduxYREVFVXrMoUOHIAiCwb/IyMgGirrxWLx4sUE9uLm5VXoM7z0tX1/fcu+jV199tdz9m/p9d+TIEYwaNQoeHh4QBAFbt27VKxdFEYsXL4aHhwcsLCzQv39/XLly5b7n3bRpEwIDA2FmZobAwEBs2bKlnt6B8VRWdyqVCm+//TaCg4NhZWUFDw8PTJ48GcnJyZWec+3ateXejyUlJfX8bhrW/e67qVOnGtRBjx497nvepnDfAfevv/LuIUEQ8L///a/CczaVe68qzycP4u89JgX17M8//8Ts2bPx3nvv4fz58+jbty+GDx+O+Pj4cvePiYnBiBEj0LdvX5w/fx7vvvsuXnvtNWzatKmBIze+w4cP49VXX8WJEycQFhaG0tJShIaGoqio6L7HRkVFISUlRfevZcuWDRBx49OuXTu9eoiIiKhwX957d5w+fVqv3sLCwgAATz31VKXHNdX7rqioCB06dMDq1avLLf/888/x5ZdfYvXq1Th9+jTc3NwwZMgQFBQUVHjO48ePY/z48Zg0aRIuXryISZMmYdy4cTh58mR9vQ2jqKzu5HI5zp07hwULFuDcuXPYvHkzrl+/jtGjR9/3vLa2tnr3YkpKCszNzevjLRjN/e47ABg2bJheHfzzzz+VnrOp3HfA/evv3vvn559/hiAIeOKJJyo9b1O496ryfPJA/t4TqV5169ZNfOmll/S2tWnTRnznnXfK3X/evHlimzZt9La9+OKLYo8ePeotxgdFenq6CEA8fPhwhfscPHhQBCDm5OQ0XGCN1KJFi8QOHTpUeX/eexV7/fXXRX9/f1Gj0ZRbzvvuDgDili1bdK81Go3o5uYmfvrpp7ptJSUlop2dnbhmzZoKzzNu3Dhx2LBhetuGDh0qTpgwoc5jbizurbvynDp1SgQgxsXFVbjPL7/8ItrZ2dVtcI1ceXU3ZcoUccyYMdU6T1O870SxavfemDFjxIEDB1a6T1O890TR8PnkQf29x5aCeqRUKnH27FmEhobqbQ8NDcWxY8fKPeb48eMG+w8dOhRnzpyBSqWqt1gfBHl5eQAABweH++7bqVMnuLu7Y9CgQTh48GB9h9Zo3bhxAx4eHvDz88OECRNw69atCvflvVc+pVKJdevW4bnnnoMgCJXuy/vOUExMDFJTU/XuLTMzM/Tr16/C34NAxfdjZcc0BXl5eRAEAc2aNat0v8LCQvj4+MDLywsjR47E+fPnGybARubQoUNwcXFBq1atMGPGDKSnp1e6P++78qWlpWHXrl2YPn36ffdtivfevc8nD+rvPSYF9SgzMxNqtRqurq56211dXZGamlruMampqeXuX1paiszMzHqLtbETRRFz5sxBnz59EBQUVOF+7u7u+P7777Fp0yZs3rwZrVu3xqBBg3DkyJEGjLZx6N69O3777Tfs3bsXP/zwA1JTU9GrVy9kZWWVuz/vvfJt3boVubm5mDp1aoX78L6rWNnvuur8Hiw7rrrHPOxKSkrwzjvvYOLEibC1ta1wvzZt2mDt2rXYvn07/vjjD5ibm6N37964ceNGA0ZrfMOHD8f//d//4d9//8WyZctw+vRpDBw4EAqFosJjeN+V79dff4WNjQ0ef/zxSvdrivdeec8nD+rvPZMGuUoTd++ni6IoVvqJY3n7l7e9KZk5cyYuXbqE8PDwSvdr3bo1WrdurXvds2dPJCQk4IsvvsAjjzxS32E2KsOHD9d9HRwcjJ49e8Lf3x+//vor5syZU+4xvPcM/fTTTxg+fDg8PDwq3If33f1V9/dgTY95WKlUKkyYMAEajQbffPNNpfv26NFDb0Bt79690blzZ6xatQorV66s71AbjfHjx+u+DgoKQpcuXeDj44Ndu3ZV+nDL+87Qzz//jGeeeea+YwOa4r1X2fPJg/Z7jy0F9cjJyQlSqdQgw0tPTzfIBMu4ubmVu7+JiQkcHR3rLdbGbNasWdi+fTsOHjwILy+vah/fo0ePh/pTiqqysrJCcHBwhXXBe89QXFwc9u/fj+eff77ax/K+0yqb8ao6vwfLjqvuMQ8rlUqFcePGISYmBmFhYZW2EpRHIpGga9euTf5+dHd3h4+PT6X1wPvO0NGjRxEVFVWj34MP+71X0fPJg/p7j0lBPTI1NUVISIhu5pIyYWFh6NWrV7nH9OzZ02D/ffv2oUuXLpDJZPUWa2MkiiJmzpyJzZs3499//4Wfn1+NznP+/Hm4u7vXcXQPHoVCgWvXrlVYF7z3DP3yyy9wcXHBo48+Wu1jed9p+fn5wc3t/9u715Cotj4M4M+ccaYcK4sSNa9UjhZUWFHYzYLQgggSLcrSjCIqDcsyQcL6EkZQJMRUIBYSTveIMqPImVJLzLQso6aa0QpJsisZFs7/fDjHzTve6pw39eh+fjAf3HvttfZarNnO4+y99HGZW9+/f4fVau3yOgh0PR+7O2YgagsENpsNN27c+FcBXURQXV2t+vnY1NSEV69edTsOnHcd5ebmYurUqZg8efI/Pnagzr2ffT7pt9e9XnmcWcXMZrPodDrJzc2V2tpaSU1NFQ8PD3E4HCIikpGRIatXr1bKv3z5UgwGg2zdulVqa2slNzdXdDqdnD17tq+60Gc2btwonp6eYrFYpKGhQXk1NzcrZdqP38GDB+XChQvy7NkzefTokWRkZAgAOXfuXF90oU+lpaWJxWKRly9fyt27d2Xx4sUydOhQzr1f1NraKoGBgbJz584O+zjvXH358kWqqqqkqqpKAMiBAwekqqpKWSEnOztbPD095fz581JTUyMrVqwQX19f+fz5s1LH6tWrXVZlKy0tFa1WK9nZ2fLkyRPJzs4WNzc3uXv3bq/3ryd1N3Y/fvyQJUuWiL+/v1RXV7tcB1taWpQ62o/d7t27paioSF68eCFVVVWSlJQkbm5uUl5e3hdd7DHdjd2XL18kLS1NysrKxG63S3FxsURERIifnx/n3d9+9r4VEfn06ZMYDAYxmUyd1qHWufcrn0/643WPoaAXHD58WIKCgkSv18uUKVNcltRMTEyUyMhIl/IWi0XCw8NFr9dLcHBwl2/GgQ5Ap6+8vDylTPvx27dvn4wdO1YGDx4sI0aMkNmzZ8uVK1d6/+T/A5YvXy6+vr6i0+lk9OjREhMTI48fP1b2c+5179q1awJAnj592mEf552rtiVZ278SExNF5K/l+bKyssTHx0cGDRokc+fOlZqaGpc6IiMjlfJtzpw5I6GhoaLT6SQsLGxAhqzuxs5ut3d5HSwuLlbqaD92qampEhgYKHq9Xry8vCQqKkrKysp6v3M9rLuxa25ulqioKPHy8hKdTieBgYGSmJgo9fX1LnWodd6J/Px9KyJy9OhRcXd3l48fP3Zah1rn3q98PumP1z2NyN9PEhIRERERkSrxmQIiIiIiIpVjKCAiIiIiUjmGAiIiIiIilWMoICIiIiJSOYYCIiIiIiKVYyggIiIiIlI5hgIiIiIiIpVjKCAiIiIiUjmGAiIilbNYLNBoNPj48WOftH/z5k2EhYXB6XT2eFs1NTXw9/fH169fe7wtIqL+hKGAiEhF5s2bh9TUVJdtM2fORENDAzw9PfvknNLT05GZmYk//uj5X0kTJ07E9OnTcfDgwR5vi4ioP2EoICJSOb1eDx8fH2g0ml5vu6ysDDabDXFxcb3WZlJSEkwmE1pbW3utTSKi/zqGAiIilVizZg2sVisOHToEjUYDjUYDh8PR4fah48ePY/jw4bh8+TJCQ0NhMBgQGxuLr1+/4sSJEwgODsaIESOQkpLi8sH6+/fvSE9Ph5+fHzw8PDBjxgxYLJZuz8lsNiMqKgqDBw9Wtj148ADz58/H0KFDMWzYMEydOhX37t1T9peVlWHu3Llwd3dHQEAAtmzZ4nI7UEtLC9LT0xEQEIBBgwYhJCQEubm5yv7o6Gg0NTXBarX+nyNKRDRwMBQQEanEoUOHEBERgfXr16OhoQENDQ0ICAjotGxzczNycnJgNptRVFQEi8WCmJgYFBYWorCwEPn5+Th27BjOnj2rHJOUlITS0lKYzWY8fPgQcXFxWLhwIWw2W5fndOvWLUybNs1lW3x8PPz9/VFRUYHKykpkZGRAp9MB+OuZgOjoaMTExODhw4c4deoUSkpKkJycrByfkJAAs9mMnJwcPHnyBEeOHMGQIUOU/Xq9HpMnT8bt27f/1TgSEQ1Ebn19AkRE1Ds8PT2h1+thMBjg4+PTbdkfP37AZDJh7NixAIDY2Fjk5+fj7du3GDJkCCZMmID58+ejuLgYy5cvx4sXL1BQUIDXr19j9OjRAIDt27ejqKgIeXl52Lt3b6ftOBwOpXyb+vp67NixA2FhYQCAkJAQZd/+/fuxcuVK5bmIkJAQ5OTkIDIyEiaTCfX19Th9+jSuX7+OBQsWAADGjBnToV0/Pz84HI6fDxoRkUowFBARUQcGg0EJBADg7e2N4OBgl7+4e3t7o7GxEQBw//59iAiMRqNLPS0tLRg5cmSX7Xz79s3l1iEA2LZtG9atW4f8/HwsWLAAcXFxyrlUVlbi+fPnOHnypFJeROB0OmG321FTUwOtVovIyMhu++fu7o7m5uafjAIRkXowFBARUQdtt+u00Wg0nW5rW0bU6XRCq9WisrISWq3Wpdz/Bon2Ro0ahQ8fPrhs2717N1auXIkrV67g6tWryMrKgtlsxtKlS+F0OrFhwwZs2bKlQ12BgYF4/vz5L/Xv/fv3LqGHiEjtGAqIiFREr9f3yKo74eHhaG1tRWNjI+bMmfOPjqutre2w3Wg0wmg0YuvWrVixYgXy8vKwdOlSTJkyBY8fP8a4ceM6rW/ixIlwOp2wWq3K7UOdefToEWJjY3/5PImIBjo+aExEpCLBwcEoLy+Hw+HAu3fvfts/DDMajYiPj0dCQgLOnz8Pu92OiooK7Nu3D4WFhV0eFx0djZKSEuXnb9++ITk5GRaLBXV1dSgtLUVFRQXGjx8PANi5cyfu3LmDzZs3o7q6GjabDZcuXUJKSorSv8TERKxduxYXL16E3W6HxWLB6dOnlTYcDgfevHnTbWggIlIbhgIiIhXZvn07tFotJkyYAC8vL9TX1/+2uvPy8pCQkIC0tDSEhoZiyZIlKC8v73KFIwBYtWoVamtr8fTpUwCAVqtFU1MTEhISYDQasWzZMixatAh79uwBAEyaNAlWqxU2mw1z5sxBeHg4du3aBV9fX6VOk8mE2NhYbNq0CWFhYVi/fr3LkqUFBQWIiopCUFDQb+s7EVF/pxER6euTICIi9UpPT8enT59w9OjRHm+rpaUFISEhKCgowKxZs3q8PSKi/oLfFBARUZ/KzMxEUFBQr/yH4bq6OmRmZjIQEBG1w28KiIiIiIhUjt8UEBERERGpHEMBEREREZHKMRQQEREREakcQwERERERkcoxFBARERERqRxDARERERGRyjEUEBERERGpHEMBEREREZHKMRQQEREREancn8oKfnhPAGOoAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from filterpy.common import Q_discrete_white_noise\n",
    "from filterpy.kalman import ExtendedKalmanFilter\n",
    "from numpy import eye, array, asarray\n",
    "import numpy as np\n",
    "\n",
    "dt = 0.05\n",
    "rk = ExtendedKalmanFilter(dim_x=3, dim_z=1)\n",
    "radar = RadarSim(dt, pos=0., vel=100., alt=1000.)\n",
    "\n",
    "# make an imperfect starting guess\n",
    "rk.x = array([radar.pos-100, radar.vel+100, radar.alt+1000])\n",
    "\n",
    "rk.F = eye(3) + array([[0, 1, 0],\n",
    "                       [0, 0, 0],\n",
    "                       [0, 0, 0]]) * dt\n",
    "\n",
    "range_std = 5. # meters\n",
    "rk.R = np.diag([range_std**2])\n",
    "rk.Q[0:2, 0:2] = Q_discrete_white_noise(2, dt=dt, var=0.1)\n",
    "rk.Q[2,2] = 0.1\n",
    "rk.P *= 50\n",
    "\n",
    "xs, track = [], []\n",
    "for i in range(int(20/dt)):\n",
    "    z = radar.get_range()\n",
    "    track.append((radar.pos, radar.vel, radar.alt))\n",
    "    \n",
    "    rk.update(array([z]), HJacobian_at, hx)\n",
    "    xs.append(rk.x)\n",
    "    rk.predict()\n",
    "\n",
    "xs = asarray(xs)\n",
    "track = asarray(track)\n",
    "time = np.arange(0, len(xs)*dt, dt)\n",
    "ekf_internal.plot_radar(xs, track, time)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using SymPy to compute Jacobians\n",
    "\n",
    "Depending on your experience with derivatives you may have found the computation of the Jacobian difficult. Even if you found it easy, a slightly more difficult problem easily leads to very difficult computations.\n",
    "\n",
    "As explained in Appendix A, we can use the SymPy package to compute the Jacobian for us."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}x\\\\x_{vel}\\\\y\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡ x  ⎤\n",
       "⎢    ⎥\n",
       "⎢xᵥₑₗ⎥\n",
       "⎢    ⎥\n",
       "⎣ y  ⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{x}{\\sqrt{x^{2} + y^{2}}} & 0 & \\frac{y}{\\sqrt{x^{2} + y^{2}}}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡     x                y      ⎤\n",
       "⎢────────────  0  ────────────⎥\n",
       "⎢   _________        _________⎥\n",
       "⎢  ╱  2    2        ╱  2    2 ⎥\n",
       "⎣╲╱  x  + y       ╲╱  x  + y  ⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import sympy\n",
    "from IPython.display import display\n",
    "sympy.init_printing(use_latex='mathjax')\n",
    "\n",
    "x, x_vel, y = sympy.symbols('x, x_vel y')\n",
    "\n",
    "H = sympy.Matrix([sympy.sqrt(x**2 + y**2)])\n",
    "\n",
    "state = sympy.Matrix([x, x_vel, y])\n",
    "J = H.jacobian(state)\n",
    "\n",
    "display(state)\n",
    "display(J)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This result is the same as the result we computed above, and with much less effort on our part!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Robot Localization\n",
    "\n",
    "It's time to try a real problem. I warn you that this section is difficult. However, most books choose simple, textbook problems with simple answers, and you are left wondering how to solve a real world problem. \n",
    "\n",
    "We will consider the problem of robot localization. We already implemented this in the **Unscented Kalman Filter** chapter, and I recommend you read it now if you haven't already.  In this scenario we have a robot that is moving through a landscape using a sensor to detect landmarks. This could be a self driving car using computer vision to identify trees, buildings, and other landmarks. It might be one of those small robots that vacuum your house, or a robot in a warehouse.\n",
    "\n",
    "The robot has 4 wheels in the same configuration used by automobiles. It maneuvers by pivoting the front wheels. This causes the robot to pivot around the rear axle while moving forward. This is nonlinear behavior which we will have to model. \n",
    "\n",
    "The robot has a sensor that measures the range and bearing to known targets in the landscape. This is nonlinear because computing a position from a range and bearing requires square roots and trigonometry. \n",
    "\n",
    "Both the process model and measurement models are nonlinear. The EKF accommodates both, so we provisionally conclude that the EKF is a viable choice for this problem."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Robot Motion Model\n",
    "\n",
    "At a first approximation an automobile steers by pivoting the front tires while moving forward. The front of the car moves in the direction that the wheels are pointing while pivoting around the rear tires. This simple description is complicated by issues such as slippage due to friction, the differing behavior of the rubber tires at different speeds, and the need for the outside tire to travel a different radius than the inner tire. Accurately modeling steering requires a complicated set of differential equations. \n",
    "\n",
    "For lower speed robotic applications a simpler *bicycle model* has been found to perform well. This is a depiction of the model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ekf_internal.plot_bicycle()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the **Unscented Kalman Filter** chapter we derived these equations:\n",
    "\n",
    "$$\\begin{aligned} \n",
    "\\beta &= \\frac d w \\tan(\\alpha) \\\\\n",
    "x &= x - R\\sin(\\theta) + R\\sin(\\theta + \\beta) \\\\\n",
    "y &= y + R\\cos(\\theta) - R\\cos(\\theta + \\beta) \\\\\n",
    "\\theta &= \\theta + \\beta\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "where $\\theta$ is the robot's heading.\n",
    "\n",
    "You do not need to understand this model in detail if you are not interested in steering models. The important thing to recognize is that our motion model is nonlinear, and we will need to deal with that with our Kalman filter."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Design the State Variables\n",
    "\n",
    "For our filter we will maintain the position $x,y$ and orientation $\\theta$ of the robot:\n",
    "\n",
    "$$\\mathbf x = \\begin{bmatrix}x \\\\ y \\\\ \\theta\\end{bmatrix}$$\n",
    "\n",
    "Our control input $\\mathbf u$ is the velocity $v$ and steering angle $\\alpha$:\n",
    "\n",
    "$$\\mathbf u = \\begin{bmatrix}v \\\\ \\alpha\\end{bmatrix}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Design the System Model\n",
    "\n",
    "We model our system as a nonlinear motion model plus noise.\n",
    "\n",
    "$$\\bar x = f(x, u) + \\mathcal{N}(0, Q)$$\n",
    "\n",
    "\n",
    "\n",
    "Using the motion model for a robot that we created above, we can expand this to\n",
    "\n",
    "$$\\bar{\\begin{bmatrix}x\\\\y\\\\\\theta\\end{bmatrix}} = \\begin{bmatrix}x\\\\y\\\\\\theta\\end{bmatrix} + \n",
    "\\begin{bmatrix}- R\\sin(\\theta) + R\\sin(\\theta + \\beta) \\\\\n",
    "R\\cos(\\theta) - R\\cos(\\theta + \\beta) \\\\\n",
    "\\beta\\end{bmatrix}$$\n",
    "\n",
    "We find The $\\mathbf F$ by taking the Jacobian of $f(x,u)$.\n",
    "\n",
    "$$\\mathbf F = \\frac{\\partial f(x, u)}{\\partial x} =\\begin{bmatrix}\n",
    "\\frac{\\partial f_1}{\\partial x} & \n",
    "\\frac{\\partial f_1}{\\partial y} &\n",
    "\\frac{\\partial f_1}{\\partial \\theta}\\\\\n",
    "\\frac{\\partial f_2}{\\partial x} & \n",
    "\\frac{\\partial f_2}{\\partial y} &\n",
    "\\frac{\\partial f_2}{\\partial \\theta} \\\\\n",
    "\\frac{\\partial f_3}{\\partial x} & \n",
    "\\frac{\\partial f_3}{\\partial y} &\n",
    "\\frac{\\partial f_3}{\\partial \\theta}\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "When we calculate these we get\n",
    "\n",
    "$$\\mathbf F = \\begin{bmatrix}\n",
    "1 & 0 & -R\\cos(\\theta) + R\\cos(\\theta+\\beta) \\\\\n",
    "0 & 1 & -R\\sin(\\theta) + R\\sin(\\theta+\\beta) \\\\\n",
    "0 & 0 & 1\n",
    "\\end{bmatrix}$$\n",
    "\n",
    "We can double check our work with SymPy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1 & 0 & - \\frac{w \\cos{\\left(\\theta \\right)}}{\\tan{\\left(\\alpha \\right)}} + \\frac{w \\cos{\\left(\\frac{t v \\tan{\\left(\\alpha \\right)}}{w} + \\theta \\right)}}{\\tan{\\left(\\alpha \\right)}}\\\\0 & 1 & - \\frac{w \\sin{\\left(\\theta \\right)}}{\\tan{\\left(\\alpha \\right)}} + \\frac{w \\sin{\\left(\\frac{t v \\tan{\\left(\\alpha \\right)}}{w} + \\theta \\right)}}{\\tan{\\left(\\alpha \\right)}}\\\\0 & 0 & 1\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡                        ⎛t⋅v⋅tan(α)    ⎞⎤\n",
       "⎢                   w⋅cos⎜────────── + θ⎟⎥\n",
       "⎢        w⋅cos(θ)        ⎝    w         ⎠⎥\n",
       "⎢1  0  - ──────── + ─────────────────────⎥\n",
       "⎢         tan(α)            tan(α)       ⎥\n",
       "⎢                                        ⎥\n",
       "⎢                        ⎛t⋅v⋅tan(α)    ⎞⎥\n",
       "⎢                   w⋅sin⎜────────── + θ⎟⎥\n",
       "⎢        w⋅sin(θ)        ⎝    w         ⎠⎥\n",
       "⎢0  1  - ──────── + ─────────────────────⎥\n",
       "⎢         tan(α)            tan(α)       ⎥\n",
       "⎢                                        ⎥\n",
       "⎣0  0                  1                 ⎦"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sympy\n",
    "from sympy.abc import alpha, x, y, v, w, R, theta\n",
    "from sympy import symbols, Matrix\n",
    "sympy.init_printing(use_latex=\"mathjax\", fontsize='16pt')\n",
    "time = symbols('t')\n",
    "d = v*time\n",
    "beta = (d/w)*sympy.tan(alpha)\n",
    "r = w/sympy.tan(alpha)\n",
    "\n",
    "fxu = Matrix([[x-r*sympy.sin(theta) + r*sympy.sin(theta+beta)],\n",
    "              [y+r*sympy.cos(theta)- r*sympy.cos(theta+beta)],\n",
    "              [theta+beta]])\n",
    "F = fxu.jacobian(Matrix([x, y, theta]))\n",
    "F"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That looks a bit complicated. We can use SymPy to substitute terms:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1 & 0 & - R \\cos{\\left(\\theta \\right)} + R \\cos{\\left(\\beta + \\theta \\right)}\\\\0 & 1 & - R \\sin{\\left(\\theta \\right)} + R \\sin{\\left(\\beta + \\theta \\right)}\\\\0 & 0 & 1\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡1  0  -R⋅cos(θ) + R⋅cos(β + θ)⎤\n",
       "⎢                              ⎥\n",
       "⎢0  1  -R⋅sin(θ) + R⋅sin(β + θ)⎥\n",
       "⎢                              ⎥\n",
       "⎣0  0             1            ⎦"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# reduce common expressions\n",
    "B, R = symbols('beta, R')\n",
    "F = F.subs((d/w)*sympy.tan(alpha), B)\n",
    "F.subs(w/sympy.tan(alpha), R)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This form  verifies that the computation of the Jacobian is correct.\n",
    "\n",
    "Now we can turn our attention to the noise. Here, the noise is in our control input, so it is in *control space*. In other words, we command a specific velocity and steering angle, but we need to convert that into errors in $x, y, \\theta$. In a real system this might vary depending on velocity, so it will need to be recomputed for every prediction. I will choose this as the noise model; for a real robot you will need to choose a model that accurately depicts the error in your system. \n",
    "\n",
    "$$\\mathbf{M} = \\begin{bmatrix}\\sigma_{vel}^2 & 0 \\\\ 0 & \\sigma_\\alpha^2\\end{bmatrix}$$\n",
    "\n",
    "If this was a linear problem we would convert from control space to state space using the by now familiar $\\mathbf{FMF}^\\mathsf T$ form. Since our motion model is nonlinear we do not try to find a closed form solution to this, but instead linearize it with a Jacobian which we will name $\\mathbf{V}$. \n",
    "\n",
    "$$\\mathbf{V} = \\frac{\\partial f(x, u)}{\\partial u} \\begin{bmatrix}\n",
    "\\frac{\\partial f_1}{\\partial v} & \\frac{\\partial f_1}{\\partial \\alpha} \\\\\n",
    "\\frac{\\partial f_2}{\\partial v} & \\frac{\\partial f_2}{\\partial \\alpha} \\\\\n",
    "\\frac{\\partial f_3}{\\partial v} & \\frac{\\partial f_3}{\\partial \\alpha}\n",
    "\\end{bmatrix}$$\n",
    "\n",
    "These partial derivatives become very difficult to work with. Let's compute them with SymPy. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}t \\cos{\\left(\\beta + \\theta \\right)} & \\frac{d \\left(\\tan^{2}{\\left(\\alpha \\right)} + 1\\right) \\cos{\\left(\\beta + \\theta \\right)}}{\\tan{\\left(\\alpha \\right)}} - \\frac{w \\left(- \\tan^{2}{\\left(\\alpha \\right)} - 1\\right) \\sin{\\left(\\theta \\right)}}{\\tan^{2}{\\left(\\alpha \\right)}} + \\frac{w \\left(- \\tan^{2}{\\left(\\alpha \\right)} - 1\\right) \\sin{\\left(\\beta + \\theta \\right)}}{\\tan^{2}{\\left(\\alpha \\right)}}\\\\t \\sin{\\left(\\beta + \\theta \\right)} & \\frac{d \\left(\\tan^{2}{\\left(\\alpha \\right)} + 1\\right) \\sin{\\left(\\beta + \\theta \\right)}}{\\tan{\\left(\\alpha \\right)}} + \\frac{w \\left(- \\tan^{2}{\\left(\\alpha \\right)} - 1\\right) \\cos{\\left(\\theta \\right)}}{\\tan^{2}{\\left(\\alpha \\right)}} - \\frac{w \\left(- \\tan^{2}{\\left(\\alpha \\right)} - 1\\right) \\cos{\\left(\\beta + \\theta \\right)}}{\\tan^{2}{\\left(\\alpha \\right)}}\\\\\\frac{t}{R} & \\frac{d \\left(\\tan^{2}{\\left(\\alpha \\right)} + 1\\right)}{w}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡                ⎛   2       ⎞                ⎛     2       ⎞            ⎛    \n",
       "⎢              d⋅⎝tan (α) + 1⎠⋅cos(β + θ)   w⋅⎝- tan (α) - 1⎠⋅sin(θ)   w⋅⎝- ta\n",
       "⎢t⋅cos(β + θ)  ────────────────────────── - ──────────────────────── + ───────\n",
       "⎢                        tan(α)                        2                      \n",
       "⎢                                                   tan (α)                   \n",
       "⎢                                                                             \n",
       "⎢                ⎛   2       ⎞                ⎛     2       ⎞            ⎛    \n",
       "⎢              d⋅⎝tan (α) + 1⎠⋅sin(β + θ)   w⋅⎝- tan (α) - 1⎠⋅cos(θ)   w⋅⎝- ta\n",
       "⎢t⋅sin(β + θ)  ────────────────────────── + ──────────────────────── - ───────\n",
       "⎢                        tan(α)                        2                      \n",
       "⎢                                                   tan (α)                   \n",
       "⎢                                                                             \n",
       "⎢                                                  ⎛   2       ⎞              \n",
       "⎢     t                                          d⋅⎝tan (α) + 1⎠              \n",
       "⎢     ─                                          ───────────────              \n",
       "⎣     R                                                 w                     \n",
       "\n",
       " 2       ⎞           ⎤\n",
       "n (α) - 1⎠⋅sin(β + θ)⎥\n",
       "─────────────────────⎥\n",
       "      2              ⎥\n",
       "   tan (α)           ⎥\n",
       "                     ⎥\n",
       " 2       ⎞           ⎥\n",
       "n (α) - 1⎠⋅cos(β + θ)⎥\n",
       "─────────────────────⎥\n",
       "      2              ⎥\n",
       "   tan (α)           ⎥\n",
       "                     ⎥\n",
       "                     ⎥\n",
       "                     ⎥\n",
       "                     ⎥\n",
       "                     ⎦"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "V = fxu.jacobian(Matrix([v, alpha]))\n",
    "V = V.subs(sympy.tan(alpha)/w, 1/R) \n",
    "V = V.subs(time*v/R, B)\n",
    "V = V.subs(time*v, 'd')\n",
    "V"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This should give you an appreciation of how quickly the EKF become mathematically intractable. \n",
    "\n",
    "This gives us the final form of our prediction equations:\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\mathbf{\\bar x} &= \\mathbf x + \n",
    "\\begin{bmatrix}- R\\sin(\\theta) + R\\sin(\\theta + \\beta) \\\\\n",
    "R\\cos(\\theta) - R\\cos(\\theta + \\beta) \\\\\n",
    "\\beta\\end{bmatrix}\\\\\n",
    "\\mathbf{\\bar P} &=\\mathbf{FPF}^{\\mathsf T} + \\mathbf{VMV}^{\\mathsf T}\n",
    "\\end{aligned}$$\n",
    "\n",
    "This form of linearization is not the only way to predict $\\mathbf x$. For example, we could use a numerical integration technique such as *Runge Kutta* to compute the movement\n",
    "of the robot. This will be required if the time step is relatively large. Things are not as cut and dried with the EKF as for the Kalman filter. For a real problem you have to carefully model your system with differential equations and then determine the most appropriate way to solve that system. The correct approach depends on the accuracy you require, how nonlinear the equations are, your processor budget, and numerical stability concerns."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Design the Measurement Model\n",
    "\n",
    "The robot's sensor provides a noisy bearing and range measurement to multiple known locations in the landscape. The measurement model must convert the state $\\begin{bmatrix}x & y&\\theta\\end{bmatrix}^\\mathsf T$ into a range and bearing to the landmark. If $\\mathbf p$ \n",
    "is the position of a landmark, the range $r$ is\n",
    "\n",
    "$$r = \\sqrt{(p_x - x)^2 + (p_y - y)^2}$$\n",
    "\n",
    "The sensor provides bearing relative to the orientation of the robot, so we must subtract the robot's orientation from the bearing to get the sensor reading, like so:\n",
    "\n",
    "$$\\phi = \\arctan(\\frac{p_y - y}{p_x - x}) - \\theta$$\n",
    "\n",
    "\n",
    "Thus our measurement model $h$ is\n",
    "\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\mathbf z& = h(\\bar{\\mathbf x}, \\mathbf p) &+ \\mathcal{N}(0, R)\\\\\n",
    "&= \\begin{bmatrix}\n",
    "\\sqrt{(p_x - x)^2 + (p_y - y)^2} \\\\\n",
    "\\arctan(\\frac{p_y - y}{p_x - x}) - \\theta \n",
    "\\end{bmatrix} &+ \\mathcal{N}(0, R)\n",
    "\\end{aligned}$$\n",
    "\n",
    "This is clearly nonlinear, so we need linearize $h$  at $\\mathbf x$ by taking its Jacobian. We compute that with SymPy below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{- p_{x} + x}{\\sqrt{\\left(p_{x} - x\\right)^{2} + \\left(p_{y} - y\\right)^{2}}} & \\frac{- p_{y} + y}{\\sqrt{\\left(p_{x} - x\\right)^{2} + \\left(p_{y} - y\\right)^{2}}} & 0\\\\- \\frac{- p_{y} + y}{\\left(p_{x} - x\\right)^{2} + \\left(p_{y} - y\\right)^{2}} & - \\frac{p_{x} - x}{\\left(p_{x} - x\\right)^{2} + \\left(p_{y} - y\\right)^{2}} & -1\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡          -pₓ + x                      -p_y + y             ⎤\n",
       "⎢───────────────────────────  ───────────────────────────  0 ⎥\n",
       "⎢   ________________________     ________________________    ⎥\n",
       "⎢  ╱         2            2     ╱         2            2     ⎥\n",
       "⎢╲╱  (pₓ - x)  + (p_y - y)    ╲╱  (pₓ - x)  + (p_y - y)      ⎥\n",
       "⎢                                                            ⎥\n",
       "⎢       -(-p_y + y)                   -(pₓ - x)              ⎥\n",
       "⎢  ──────────────────────       ──────────────────────     -1⎥\n",
       "⎢          2            2               2            2       ⎥\n",
       "⎣  (pₓ - x)  + (p_y - y)        (pₓ - x)  + (p_y - y)        ⎦"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "px, py = symbols('p_x, p_y')\n",
    "z = Matrix([[sympy.sqrt((px-x)**2 + (py-y)**2)],\n",
    "            [sympy.atan2(py-y, px-x) - theta]])\n",
    "z.jacobian(Matrix([x, y, theta]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we need to write that as a Python function. For example we might write:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import sqrt\n",
    "\n",
    "def H_of(x, landmark_pos):\n",
    "    \"\"\" compute Jacobian of H matrix where h(x) computes \n",
    "    the range and bearing to a landmark for state x \"\"\"\n",
    "\n",
    "    px = landmark_pos[0]\n",
    "    py = landmark_pos[1]\n",
    "    hyp = (px - x[0, 0])**2 + (py - x[1, 0])**2\n",
    "    dist = sqrt(hyp)\n",
    "\n",
    "    H = array(\n",
    "        [[-(px - x[0, 0]) / dist, -(py - x[1, 0]) / dist, 0],\n",
    "         [ (py - x[1, 0]) / hyp,  -(px - x[0, 0]) / hyp, -1]])\n",
    "    return H"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We also need to define a function that converts the system state into a measurement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import atan2\n",
    "\n",
    "def Hx(x, landmark_pos):\n",
    "    \"\"\" takes a state variable and returns the measurement\n",
    "    that would correspond to that state.\n",
    "    \"\"\"\n",
    "    px = landmark_pos[0]\n",
    "    py = landmark_pos[1]\n",
    "    dist = sqrt((px - x[0, 0])**2 + (py - x[1, 0])**2)\n",
    "\n",
    "    Hx = array([[dist],\n",
    "                [atan2(py - x[1, 0], px - x[0, 0]) - x[2, 0]]])\n",
    "    return Hx"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Design Measurement Noise\n",
    "\n",
    "It is reasonable to assume that the noise of the range and bearing measurements are independent, hence\n",
    "\n",
    "$$\\mathbf R=\\begin{bmatrix}\\sigma_{range}^2 & 0 \\\\ 0 & \\sigma_{bearing}^2\\end{bmatrix}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementation\n",
    "\n",
    "We will use `FilterPy`'s `ExtendedKalmanFilter` class to implement the filter. Its `predict()` method uses the standard linear equations for the process model. Ours is nonlinear, so we will have to override `predict()` with our own implementation.  I'll want to also use this class to simulate the robot, so I'll add a method `move()` that computes the position of the robot which both `predict()` and my simulation can call.\n",
    "\n",
    "The matrices for the prediction step are quite large. While writing this code I made several errors before I finally got it working. I only found my errors by using SymPy's `evalf` function. `evalf` evaluates a SymPy `Matrix` with specific values for the variables. I decided to demonstrate this technique to you, and used `evalf` in the Kalman filter code. You'll need to understand a couple of points.\n",
    "\n",
    "First, `evalf` uses a dictionary to specify the values. For example, if your matrix contains an `x` and `y`, you can write\n",
    "\n",
    "```python\n",
    "    M.evalf(subs={x:3, y:17})\n",
    "```\n",
    "    \n",
    "to evaluate the matrix for `x=3` and `y=17`. \n",
    "\n",
    "Second, `evalf` returns a `sympy.Matrix` object. Use `numpy.array(M).astype(float)` to convert it to a NumPy array. `numpy.array(M)` creates an array of  type `object`, which is not what you want.\n",
    "\n",
    "Here is the code for the EKF:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "from filterpy.kalman import ExtendedKalmanFilter as EKF\n",
    "from numpy import array, sqrt\n",
    "class RobotEKF(EKF):\n",
    "    def __init__(self, dt, wheelbase, std_vel, std_steer):\n",
    "        EKF.__init__(self, 3, 2, 2)\n",
    "        self.dt = dt\n",
    "        self.wheelbase = wheelbase\n",
    "        self.std_vel = std_vel\n",
    "        self.std_steer = std_steer\n",
    "\n",
    "        a, x, y, v, w, theta, time = symbols(\n",
    "            'a, x, y, v, w, theta, t')\n",
    "        d = v*time\n",
    "        beta = (d/w)*sympy.tan(a)\n",
    "        r = w/sympy.tan(a)\n",
    "    \n",
    "        self.fxu = Matrix(\n",
    "            [[x-r*sympy.sin(theta)+r*sympy.sin(theta+beta)],\n",
    "             [y+r*sympy.cos(theta)-r*sympy.cos(theta+beta)],\n",
    "             [theta+beta]])\n",
    "\n",
    "        self.F_j = self.fxu.jacobian(Matrix([x, y, theta]))\n",
    "        self.V_j = self.fxu.jacobian(Matrix([v, a]))\n",
    "\n",
    "        # save dictionary and it's variables for later use\n",
    "        self.subs = {x: 0, y: 0, v:0, a:0, \n",
    "                     time:dt, w:wheelbase, theta:0}\n",
    "        self.x_x, self.x_y, = x, y \n",
    "        self.v, self.a, self.theta = v, a, theta\n",
    "\n",
    "    def predict(self, u):\n",
    "        self.x = self.move(self.x, u, self.dt)\n",
    "\n",
    "        self.subs[self.theta] = self.x[2, 0]\n",
    "        self.subs[self.v] = u[0]\n",
    "        self.subs[self.a] = u[1]\n",
    "\n",
    "        F = array(self.F_j.evalf(subs=self.subs)).astype(float)\n",
    "        V = array(self.V_j.evalf(subs=self.subs)).astype(float)\n",
    "\n",
    "        # covariance of motion noise in control space\n",
    "        M = array([[self.std_vel*u[0]**2, 0], \n",
    "                   [0, self.std_steer**2]])\n",
    "\n",
    "        self.P = F @ self.P @ F.T + V @ M @ V.T\n",
    "\n",
    "    def move(self, x, u, dt):\n",
    "        hdg = x[2, 0]\n",
    "        vel = u[0]\n",
    "        steering_angle = u[1]\n",
    "        dist = vel * dt\n",
    "\n",
    "        if abs(steering_angle) > 0.001: # is robot turning?\n",
    "            beta = (dist / self.wheelbase) * tan(steering_angle)\n",
    "            r = self.wheelbase / tan(steering_angle) # radius\n",
    "\n",
    "            dx = np.array([[-r*sin(hdg) + r*sin(hdg + beta)], \n",
    "                           [r*cos(hdg) - r*cos(hdg + beta)], \n",
    "                           [beta]])\n",
    "        else: # moving in straight line\n",
    "            dx = np.array([[dist*cos(hdg)], \n",
    "                           [dist*sin(hdg)], \n",
    "                           [0]])\n",
    "        return x + dx"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we have another issue to handle. The residual is notionally computed as $y = z - h(x)$ but this will not work because our measurement contains an angle in it. Suppose z has a bearing of $1^\\circ$ and $h(x)$ has a bearing of $359^\\circ$. Naively subtracting them would yield a angular difference of $-358^\\circ$, whereas the correct value is $2^\\circ$. We have to write code to correctly compute the bearing residual."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def residual(a, b):\n",
    "    \"\"\" compute residual (a-b) between measurements containing \n",
    "    [range, bearing]. Bearing is normalized to [-pi, pi)\"\"\"\n",
    "    y = a - b\n",
    "    y[1] = y[1] % (2 * np.pi)    # force in range [0, 2 pi)\n",
    "    if y[1] > np.pi:             # move to [-pi, pi)\n",
    "        y[1] -= 2 * np.pi\n",
    "    return y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The rest of the code runs the simulation and plots the results, and shouldn't need too much comment by now. I create a variable `landmarks` that contains the landmark coordinates. I update the simulated robot position 10 times a second, but run the EKF only once per second. This is for two reasons. First, we are not using Runge Kutta to integrate the differental equations of motion, so a narrow time step allows our simulation to be more accurate. Second, it is fairly normal in embedded systems to have limited processing speed. This forces you to run your Kalman filter only as frequently as absolutely needed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "from filterpy.stats import plot_covariance_ellipse\n",
    "from math import sqrt, tan, cos, sin, atan2\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "dt = 1.0\n",
    "\n",
    "def z_landmark(lmark, sim_pos, std_rng, std_brg):\n",
    "    x, y = sim_pos[0, 0], sim_pos[1, 0]\n",
    "    d = np.sqrt((lmark[0] - x)**2 + (lmark[1] - y)**2)  \n",
    "    a = atan2(lmark[1] - y, lmark[0] - x) - sim_pos[2, 0]\n",
    "    z = np.array([[d + randn()*std_rng],\n",
    "                  [a + randn()*std_brg]])\n",
    "    return z\n",
    "\n",
    "def ekf_update(ekf, z, landmark):\n",
    "    ekf.update(z, HJacobian=H_of, Hx=Hx, \n",
    "               residual=residual,\n",
    "               args=(landmark), hx_args=(landmark))\n",
    "    \n",
    "                \n",
    "def run_localization(landmarks, std_vel, std_steer, \n",
    "                     std_range, std_bearing,\n",
    "                     step=10, ellipse_step=20, ylim=None):\n",
    "    ekf = RobotEKF(dt, wheelbase=0.5, std_vel=std_vel, \n",
    "                   std_steer=std_steer)\n",
    "    ekf.x = array([[2, 6, .3]]).T # x, y, steer angle\n",
    "    ekf.P = np.diag([.1, .1, .1])\n",
    "    ekf.R = np.diag([std_range**2, std_bearing**2])\n",
    "\n",
    "    sim_pos = ekf.x.copy() # simulated position\n",
    "    # steering command (vel, steering angle radians)\n",
    "    u = array([1.1, .01]) \n",
    "\n",
    "    plt.figure()\n",
    "    plt.scatter(landmarks[:, 0], landmarks[:, 1],\n",
    "                marker='s', s=60)\n",
    "    \n",
    "    track = []\n",
    "    for i in range(200):\n",
    "        sim_pos = ekf.move(sim_pos, u, dt/10.) # simulate robot\n",
    "        track.append(sim_pos)\n",
    "\n",
    "        if i % step == 0:\n",
    "            ekf.predict(u=u)\n",
    "\n",
    "            if i % ellipse_step == 0:\n",
    "                plot_covariance_ellipse(\n",
    "                    (ekf.x[0,0], ekf.x[1,0]), ekf.P[0:2, 0:2], \n",
    "                     std=6, facecolor='k', alpha=0.3)\n",
    "\n",
    "            x, y = sim_pos[0, 0], sim_pos[1, 0]\n",
    "            for lmark in landmarks:\n",
    "                z = z_landmark(lmark, sim_pos,\n",
    "                               std_range, std_bearing)\n",
    "                ekf_update(ekf, z, lmark)\n",
    "\n",
    "            if i % ellipse_step == 0:\n",
    "                plot_covariance_ellipse(\n",
    "                    (ekf.x[0,0], ekf.x[1,0]), ekf.P[0:2, 0:2],\n",
    "                    std=6, facecolor='g', alpha=0.8)\n",
    "    track = np.array(track)\n",
    "    plt.plot(track[:, 0], track[:,1], color='k', lw=2)\n",
    "    plt.axis('equal')\n",
    "    plt.title(\"EKF Robot localization\")\n",
    "    if ylim is not None: plt.ylim(*ylim)\n",
    "    plt.show()\n",
    "    return ekf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final P: [0.025 0.042 0.002]\n"
     ]
    }
   ],
   "source": [
    "landmarks = array([[5, 10], [10, 5], [15, 15]])\n",
    "\n",
    "ekf = run_localization(\n",
    "    landmarks, std_vel=0.1, std_steer=np.radians(1),\n",
    "    std_range=0.3, std_bearing=0.1)\n",
    "print('Final P:', ekf.P.diagonal())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I have plotted the landmarks as solid squares. The path of the robot is drawn with a black line. The covariance ellipses for the predict step are light gray, and the covariances of the update are shown in green. To make them visible at this scale I have set the ellipse boundary at 6$\\sigma$.\n",
    "\n",
    "We can see that there is a lot of uncertainty added by our motion model, and that most of the error in in the direction of motion. We determine that from the shape of the blue ellipses. After a few steps we can see that the filter incorporates the landmark measurements and the errors improve.\n",
    "\n",
    "I used the same initial conditions and landmark locations in the UKF chapter. The UKF achieves much better accuracy in terms of the error ellipse. Both perform roughly as well as far as their estimate for $\\mathbf x$ is concerned. \n",
    "\n",
    "Now let's add another landmark."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final P: [0.02  0.02  0.002]\n"
     ]
    }
   ],
   "source": [
    "landmarks = array([[5, 10], [10, 5], [15, 15], [20, 5]])\n",
    "\n",
    "ekf = run_localization(\n",
    "    landmarks, std_vel=0.1, std_steer=np.radians(1),\n",
    "    std_range=0.3, std_bearing=0.1)\n",
    "plt.show()\n",
    "print('Final P:', ekf.P.diagonal())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The uncertainly in the estimates near the end of the track are smaller.  We can see the effect that multiple landmarks have on our uncertainty by only using the first two landmarks."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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gPdedNYmfTttvbzdTiD5H5qALIYQQoldsqQlRWddEOBnEVFLYc0oJm/WUhTdQGarhjtnzuOHxuei6sbebKkSfIiPoQgghhOgVm6qCAOhWCnd2Obkjl5MauIb69aNoqDNIGnH+/RGsLqvnqetOIcP//ZibXltbi6IoZGVl7e2miH5KRtCFEEII0SsGZPsB0BQNM+UAwO5KkDt6CWlDVhAxglRENrN4bTln/fbfVDdE9mZzO2Xjxo1MmTKFk08+mUik77dXfD9JQBdCCCFEryjI8mOzqWiKDT3uaTmuKJA+YDM54+ajqyEqI1tYXVbD2b/7D3XB6F5s8c4tX76cyZMns2rVKubPn8/MmTP3dpNEPyUBXQghhBC9wumwUZKbhlNzY8S9pOLOVq970hvJGz8f09ZEZWQL6ytrOefO/9DQFNtLLe7YJ598whFHHEFZWRkAw4cP5ze/+c1ebpXorySgCyGEEKLXHDamCI/dB0C0PqfN605fhLzxX2DZwlRFylhTVstPZ71MKJLY003t0Guvvca0adNobGwE4KCDDuLTTz9l8ODBe7dhot+SgC6EEEKIXnPsAUOwqRp2xUmsPrfdMg5vjNxxX2JoYSojW/hmUzXn//5VUn1gdZenn36a0047jXg8DsD06dP54IMPyMlp+2ZDiJ4iAV0IIYQQvebwMUUEvE7cNh+Jxhz0pL3dck5fZGtIj1AVLWPZ+kpufOK9Pdza7SzLYtasWVx88cUYRvMbhbPPPpvXXnsNn8+319ol9g0S0IUQQgjRa+x2jeMOHILfEQBLpamqsMOyLn+YnDELSFlxamNV/PeTb5n91qI92Npmuq5zxRVXcMstt7Qcu/rqq3n22WdxOBx7vD1i3yMBXQghhBC96tzjxmNTbbhUD5GKgVhWx2XdaUHShywnqjcRTDRyzwuf8eU3ZXusrdFolB/96Ec8/vjjLcfuueceHnjgAVRVYpPYM+RfmhBCCCF61X5D8xk/JI+AIx0j4SFSt/P522mFZXjyNtGYrKUpHuYXf3qTyrpwr7ezpqaGY445htdeew0Au93OP//5T37961+jKEqvX1+IbSSgCyGEEKLXnXPceNx2DzbFQVP5wF2Wzxq6EruvntpYBdXBJi7/4+u9+tDounXrmDRpEvPnzwcgEAjw9ttvc8455/TaNYXoiAR0IYQQQvS6UyePIifdi9+eRjKYTSK88wctVQ1yxiwCR4TqaDnLS6u46cneeWj0q6++YtKkSaxduxaAwsJCPv74Y4455pheuZ4QuyIBXQghhBC9zmZT+fGRo/E509AUGw2lI3d5jt2ZJHvUopaHRl/9+Fv+/s6SHm3Xm2++ydSpU6murgZgzJgxfP755+y33349eh0hukICuhBCCCH2iMtmHEhWwEOaPYtEYw7RhsxdnrPjQ6OhRCN3P/dJjz00+tRTT3HKKacQjUYBOOKII/jkk08oKSnpkfqF6C4J6EIIIYTYI3weJ5f94EB8zgA2xUFD6cidruiyzbaHRhuStYTjYf7fo3OIxlPdbodlWdx+++1ccsklLWucn3HGGcyZM4eMjIxu1ytET5GALoQQQog95vzj96ckN40MZzZ6JI1wTX6nzssauhKbr4HaeBVltSFue+aDbl1f13V+/vOfc8cdd7Qcu/rqq3nhhRdwuVzdqlOIntblgP7RRx8xY8YMCgsLURSFV199tU2Zb775hlNOOYW0tDT8fj+HHXYYmzZt6on2CiGEEOJ7zGZTufr0Q/HYvThVN8ENIzGNXS9hqGqQPWIphpKgPl7Nfz/5lrkL1nfp2rFYjB//+Mc89dRTLcf+8Ic/8Mc//lHWOBd9Spf/NUYiESZMmMDDDz/c7uvr1q1jypQpjBo1innz5rFkyRJuvfVWeVcqhBBCCAB+cPgIxg3OJcOZjZFwEyrv3JxvpzdKYOC3RPQQ0VSEW556j4amWKfOLSsr4+abb+att94CwOFw8Pzzz3PNNdd0+z6E6C22rp5w4okncuKJJ3b4+s0338xJJ53Evffe23JsyJAh3WudEEIIIfodVVW5/pwpnDfrZdyaj9CWYfjzt6DZd73OeVrhRuJ1edQ12XAGXdz4xHs8ds0PdnrOkiVLOPnkkykra364NC0tjVdffZWpU6f2xO0I0eO6HNB3xjRN3njjDX79619z/PHHs2jRIgYPHsyNN97Iqaee2u45iUSCRCLR8nkoFAIglUqRSnX/AZAdbaunp+oTPUf6pu+Svum7pG/6LumbzjtweB5Txhfz/uIUFdEIjZuHkDl4dZtyhmGyoTIIwKD8NDRNJXPEEioXHUldrJp3v9Z47dNvOOGQYe1eZ9tmQ+Fw806kAwcO5L///S9jxoyRfuoj9qXvm87eo2JZnXl+uoOTFYVXXnmlJXxXVlZSUFCAx+Phzjvv5Oijj+btt9/mpptu4oMPPuCoo45qU8ftt9/e6kGNbZ577jk8Hk93myaEEEKIPq68Ic6s/5XSmGwgrobIHPsOmqP1lBXTgupgEoDcNAfq1unq0dqBRDYeSEDNIsfr5/bThuJxaq3Ofeutt3jiiScwTROAESNGcNNNN5Gent7r9yZEe6LRKOeccw7BYJBAINBhuR4fQQf44Q9/yK9+9SsA9t9/fz777DMee+yxdgP6jTfe2Gr+VygUori4mOnTp++04V2RSqWYO3cu06ZNw26390idomdI3/Rd0jd9l/RN3yV903Vro+/xysffUB5JECs7mNyxX6MozSPnAIZpAc0B3el0oW1N6J6SWvRQPdGQg5SSyZfVbu697LjmcwyDG2+8kccff7zlOqeeeipnn302P/jBD6Rv+ph96ftm20yRXenRgJ6dnY3NZmPMmDGtjo8ePZpPPvmk3XOcTidOp7PNcbvd3uOd1Bt1ip4hfdN3Sd/0XdI3fZf0TefdcM4RzFu8iaieTX2jQaS2AH9uZcu0lh1trt4eboYVZZI9bDkVizJoiNfw+hcaPz5qLBOHZPHTn/601Spzv/71r/ntb3/L22+/LX3Th+0LfdPZ++vRNYUcDgcHH3wwq1atanV89erVDBw4sCcvJYQQQoh+ICfdy//7yST8jgBO1UPD+jHoyc6NHzo8cQIlq4noIWKpKNc99ApHHXVUSzjXNI3HH3+ce+65R5ZRFN8rXR5BD4fDrF27tuXz0tJSFi9eTGZmJiUlJVx33XX85Cc/4cgjj2yZg/7aa68xb968nmy3EEIIIfqJs48dxxtfrOaT5ToVkTj160czaHjztBbDNNlc1TxyXpwXQPtO0E4bsIFobQG1FSGqXn8NPdoAgN/v59///jfTp0/fszcjRA/o8tvJBQsWMHHiRCZOnAjANddcw8SJE7ntttsAOO2003jssce49957GT9+PE8++ST/+c9/mDJlSs+2XAghhBD9xl2XHEvA4ybNkUWsZgCJxlxsmtoqkGuqik1r/thGVRU8yhckPnmhJZwXFRXx2WefSTgX31tdHkGfOnUqu1r45aKLLuKiiy7qdqOEEEIIsW8pyUvjyh8ezP0vfkZUb6J+7Thc/k9AS+70vOD8IHWv1EDzM6U4Mos589o/Mm7cuD3QaiF6h0zIEkIIIUSfcOkPDmDC0Dyy3flYSQ9168Zg01SGFWUyrCiz1ci5ZVrUvl5LzX+2h3MlfzC+Kefw1uJKtlR3brUMIfoiCehCCCFEP5bSDf7z0Tdc9eAb3PG3ebz4/nKSqV3v2Lk3qKrK/VdMJ+DxkO7IJlZbSLg6v005M25SMbuCxo8aW46lHZFG4AejCVsx4skk977w6R5suRA9q0eXWRRCCCFE32FZFrc9M49/zVtBUk+gKho2zcbjr33N5accxBlTx6Aoyt5uZiuDCzK49ozDufMfHxHVw9SvG4srrR6bs3mqS6o+RcUzFSSrtk59USHnhzmkHZ6GnlxPrLaEhngtb3+1luXrqxg3JG8v3o0Q3SMj6EIIIUQ/VVUf4X+fraIhWktlbBPl0VIqwpv4dksZNz35Hlf+8Q3C0Z3P8d4bfnb8BA4fW0y2Ox9Fd1Gzaj8sC2KlMTb/eXNLOFfdKoWXFJJ2eBoANoeOb8BaInoTCT3BXf9sfw8WIfo6CehCCCFEPzX363UkEimiRhOOQCOZw5eBp4baRAU1kQrmLFjLabe9yJotdXu7qa0oisK9l08j0+8l05VLMphNxVtuyv5ahhlpnnBuz7FTdFURnmGeVuemD9iI6ojREK/lq2/L+HDxhr1wB0LsHgnoQgghRD/VFE1iAQY6nuxy/PllFEz8jIzhy4gRoiKymdVbqjjnzpdZvKZibze3lfxMH7MuOQavzYv27ddE5y2DrVPn3cPdFF1VhCPH0eY81WYRKFlN3IgQ12P8/rlPdrn6nBB9jQR0IYQQop9yObY9aqZgWc2/8hUFAvll5E34DMvZSFV0C5UNDVx47/9Y1MdC+qRRudhX/Yv4ms9bjvkOzqLwokI0t9bhef68MjRPEw2JWtaW1fPmF2v2RHOF6DES0IUQQoh+KivgRlEUNDT0mLvVay5fmPwJn6N666mOlVEbCnLxff9j2fqqvdTa1kpLS5k8eTLfLNy6GouiYt/vWPRBP8Q07Ds9V1UV0ktWkzTjxI0Yf5+zZA+0WIieIwFdCCGE6KcOHFmIAthVJ8lwepvXbY4U+eO/RPM2UB0royYY5KJ7/ss3G2v2eFt39PHHH3PIIYewfPlyADIyMpj44/9HwegTMOM+alZNYFezVjxZ1ajOGKFEIwvXVPLtpto90HIheoYEdCGEEKKfGpDtJzfDh0NzkYoEsMy2v/Y1u0H+uK/QPI1Ux8qpCga59P7XaGiK7YUWwzPPPMOxxx5LbW1zoB4xYgTz58/npQevJ9PvI8uVR6Ixh/rS4TutR1UVfPkbiBkRdDPF028t3gOtF6JnSEAXQggh+ilFURg7KAe3zQOWQrQhs91ymkMnb/yXaO4gNbFyyuqCzHzwTQzD3GNt1XWda665hosuuohUKgXAcccdxxdffMHw4cMZNiCTu39+HD6Hn4A9g3DZUMI1O1/jPJBfBqpOKNHI3K9LiSX75gZNQnyXBHQhhBCiHzvuwCE4bS40xU6kpqDDcjaHTs7YBZhajJpoBV9+W7bHduOsq6vjhBNO4I9//GPLsauuuoq33nqLjIyMlmMnHDKMS2ccSLorG5fqpW71fsTDvg7r1Rw67uxyInoTsUSKz9Y09uZtCNFjJKALIYQQ/dhJhw7H7bTj0bzE6/Mx9I5/9TvccbJGLCFhxmiI1fLMW4t5a37vroCybNkyDj74YN577z0AbDYbjz76KH/+85+x2dpueH7NGYdx1IRB5HjysVluqpcfQiLi7bB+f/4WTEsnpkf4cn2w1+5DiJ4kAV0IIYTox3weB1PGF+NzpGEZGtG6nU8L8WbV4i9eQ5PeQDjZxE1Pvk9pRUOvtO0///kPhx9+OKWlpQDk5ubywQcfcPnll3d4jqqqPHTV8YwozibfW4Sme6ledgjJqLvd8k5/I5ozSjQVZnNdgqZoolfuRYieJAFdCCGE6Od+fOQYHJoDu+IkXFW0y/IZA9fhTK+mLl5FfVMTVzzwBrF4qsfaY5omt9xyC6effjqRSASAAw88kAULFjBlypRdnu/zOPnHjacxtDCbPE8Riu6jatmhJGOuNmVVVcGZUUPcjGFaFu8tLO2x+xCit0hAF0IIIfq5o/cfRHa6F589QDKYRWIn87aheTOjnJFLUZwRamIVrCmv49d/fbdH2hIMBvnhD3/IrFmzWo799Kc/5eOPP6a4uLjT9WSne3n25tMYnJ9FnmcASspH1dLDSEQ8bcq6M2owLB3dSvHhkk09ch9C9CYJ6EIIIUQ/p2kqpx85Gp8zDVWx0bhp2K7PcejkjFqIrsSpjVby9vw1/O2dxbvVjlWrVnHooYfy+uuvA83TVf7whz/w97//Hbe7/SkqO5OX4eMfN5/GwNws8jzFKCk/VUsPJ9qQ0aqcO70egJSVZGOVzEMXfZ8EdCGEEGIfcNmMA0n3ugnY04nX5e9yFB3AFWgiY8gyYkaYUCLIAy99wZaaULeu/8Ybb3DIIYewatUqoHnzoXfeeYdrrrkGRVG6VSfAgOwAL9z2Y4YWZFHgLcZu+qlZcSiNmwe2bGak2UxUWxLT0qkNRrt9LSH2FAnoQgghxD7A53FyzrHj8DvTOz2KDhAoqMCVXU5jspZQNMoNf30Xa1fbeO7AsizuuusuZsyYQSjUHO7HjRvHggULOO6447p1L99VkOXnpd+cwYEjisj3FuPV0ghuGE3V8gNbVnhRNB0Ti5A8JCq+BySgCyGEEPuIS2ccSJrX1aVRdICsoSvBHqc2VsX8lVt48f0VnTovHA5z5plncvPNN7eE+h//+Md8/vnnDBkypNv30W4b0zw8f8uPOXPqWLLduWQ589GDBVQuOoItC6ZgJDzYFTuD8tJ69LpC9AYJ6EIIIcQ+wu9xcu6x47s8im5z6GQMWUHCjNKUDHHvC59S3RDZ6Tlr165l0qRJ/Pvf/waadzW98847+de//oXP17k3Bl1ls6nc9fNjmXXJsZRk51LoG0S6PRt7Mg+v5sepepgwLL9Xri1ET5KALoQQQuxD2o6it7/Jj26YrN1Sz9ot9eiGiS+nCmdmJY2JWhojUW6fPa/Da7z22mscdNBBLFu2DAC/389///tfbr755t2ab95ZZx49lvcfOJ+LTpzIkNwB5HkKyfbks1+xnxvPntzr1xdid0lAF0IIIfYhbUfRh3fqPEWBrGErsbQE9bEa5i5YxydLN7YqYxgGt956K6eccgrBYPNqKaNHj+bLL79kxowZPX4vO+N1O7j5p0fyxSOX8OWjP+ede85m5nEluJxtdycVoq+RgC6EEELsY7aPomcQr8snHgq0vKYbJrphYphmyzHDbD6m2OIEBq4iajQR02P8ZvY8dN0AoK6ujpNOOok777yz5bwzzjiD+fPnM2rUqD13c+3ICLgpyUvfq20QoiskoAshhBD7GL/HyXnT9iPgTMemOKhbOxbTbH6Ic0NFIxsqGtlctX05xc1VoZbjgYJN2Lwh6uPVbKwK8vArX/H1119z4IEHMmfOHAA0TeP+++/nxRdfxO/375V7FOL7TAK6EEIIsQ+aeeohFOcEyHTloEfSCFV0bhdPVVXIHLoC3UoSTDRw30MPM3nyZDZubJ7ukpuby7vvvsu11167R+abC9EfyUQsIYQQYh/ksGvcev5RXHb/a7g1H6GNo/BlVzGoIB1ontaybRS9OC+Apm4f03OnBXFlbqD+gw8wN21fcvGwww7jX//6F0VFRXv0XoTob2QEXQghhNhHHTNxMEdPHEymOxcMB/XrR2HTVGya2iqQa6rachwg1ZAiMffdVuH8op9fyocffijhXIgeIAFdCCGE2IfdfsFUAm4XaY4sYrUDiNRl77R8dE2UzQ9tJlkebz6gauQcdg5Fh5+Nw+HYAy0Wov+TgC6EEELswwqz/fzitENJc6bjUN3Urx2HkdKwaSrDijIZVpSJTVOxTIuGDxoof7IcM9q8wostw47tiB9jFg7j5Y9XUhvc+eZFQojO6XJA/+ijj5gxYwaFhYUoisKrr77aYdnLLrsMRVF48MEHd6OJQgghhOhNF520P/sNzSPbnYeVdFNfOrLV60bUoOJvFdS9VQfNi73gGeWh+JdFeIfHaUo1Eo0n+fPLX+2F1gvR/3Q5oEciESZMmMDDDz+803Kvvvoq8+fPp7CwsNuNE0IIIb7P6kJR/vLKlzzw0uc8O3cpDaHY3m5Su1RV5Z5Lj8PnchNwZBGtKiHakAlAfFOczQ9uJvpNtLmwApnTMim4oADNo5FWsg5LMQgmGmQUXYge0uVVXE488UROPPHEnZYpKyvjqquu4p133uHkk0/uduOEEEKI76tFayq48o9vUN0YwbIsVFXlDy99xozDR3LtmYeT5nPt7Sa2Mqwoi8tmHMhD/5lPTA9T++1+eBOv0fBOFTTvRYTqUck7Ow/vSG/LeQ5XAk/uZpqqNNLiGTz8ylfcfsHUvXMTQvQTPb7MommanHfeeVx33XWMHTt2l+UTiQSJRKLl81CoeUmnVCpFKpXqkTZtq6en6hM9R/qm75K+6bukb/quHfvm/hc/payugepYOQY6GjZ8sQDPzo0xb3Epv//5sRw8qm/9lfnnJ+3P+wvXk/ymibLPX6WhoqrlNddAF3nn5GFLt2FZVqvzAsVriVYXE0w08O8PV3LFjAPIDLj3dPN3Sr5v+q59qW86e489HtDvuecebDYb//d//9ep8nfffTd33HFHm+Nz5szB4/H0aNvmzp3bo/WJniN903dJ3/Rd0jd913P/eYMPvl5LMFWPoUXxFK4gFc6isbGIULKRUCSTn/zmeU49MJfjxmXt7ea2MtGzhTfm/BEzXNdyzHO4B/8xfhJagkQk0c5ZEewZ6wnWKtgbXPzmLy9x4oScPdfoLpDvm75rX+ibaDTaqXI9GtC//vprHnroIRYuXNjp3cNuvPFGrrnmmpbPQ6EQxcXFTJ8+nUAg0CPtSqVSzJ07l2nTpmG323ukTtEzpG/6Lumbvkv6pu/a1jdDx+yP5+0KGsO1eHKqyBlcCVSSjGygdtVEQlELVcnirZVhSoaO4OofH7q3m45lWTz99NPc9dtbSW39y7Zid6Hsfwy+w0P4AhU7PV8rLqeqfijYTTY0OTnppJP2RLM7Tb5v+q59qW+2zRTZlR4N6B9//DHV1dWUlJS0HDMMg2uvvZYHH3yQDRs2tDnH6XTidDrbHLfb7T3eSb1Rp+gZ0jd9l/RN3yV903dFEgYKYFommi3VMmjl9EUp3P9zateOobHawrRM/vraQmyajV+dcdhea284HOaKK67g2WefbTk2cNhoGHMGDWqShnVBnL4mnL6OHwB1ByLYPSEiCS/ryhtYW97I6IF9bxRdvm/6rn2hbzp7fz26Dvp5553H0qVLWbx4cctHYWEh1113He+8805PXkoIIYTos/ye5g17VEXFNFqPhSmaSfaI5fgGrCek19MQq+ORV7/kT//5Ym80lZUrV3LIIYe0CudXXXUV3y5byIlTDyHbk4/NclPzzQEYKW2ndXlyy4gbUQzL4MUPVuy0rBCiY10eQQ+Hw6xdu7bl89LSUhYvXkxmZiYlJSVkZbWeS2e328nPz2fkyJHfrUoIIYTol4YWNi9RqCk29Hjb56kUBTIHrwYsQmVAHP78ylcU56Zx2hGj91g7//GPf3D55Ze3zIv1+/08+eSTnHnmmQD84fJp/PCWOvSyFJVRnZpV+5E7ZiGq2v40Vl9uOaGNo4ikmnh/USm/Of+oTk95FUJs1+UR9AULFjBx4kQmTpwIwDXXXMPEiRO57bbberxxQgghxPdRTpobt8uOXXWgR/18Z9ETYFtIX9M8kp6qJ5wIcfvseazZUte2cA+LRqNccskl/OxnP2sJ5/vttx8LFixoCecAHreDR3/1AzJ8PjJduSQa8qhbN6bd+wGwO1PY/Q1EUxEqaptYV97Q6/ciRH/U5YA+depULMtq8zF79ux2y2/YsIGrr756N5sphBBCfH+oqsqo4mxcNjdmykky2v6qZNtG0p0Z1dQnqmmMRJj50JtEYslea9uyZcs4+OCDeeqpp1qOXXzxxXzxxReMGDGiTflhRZnMuvgY/M4A6Y4copUDqVs/ssOQ7kyvJWnGsYAvVm7ppbsQon/r0TnoQgghhGh28KhC3DYPoBCt7/hhSUWBnJFLUJ0RamIVrCur48Yn3uvx9liWxeOPP84hhxzCypUrAfB4PMyePZsnn3wSt7vjdctPPnwEN597BGmuDNIc2UTKB1NXOrzdkO7yN2BhkjITLFqz85VfhBDtk4AuhBBC9IKTDhuOqqg4VRex+rydltXsBtmjF6IrcWpj1bw1fw2z317cY21pbGzkzDPP5PLLLycejwMwYcIEvv76a84///xO1XH+Cfvz67Mmke7MIM2RRaRsKLVrR2GarVO6MxAEIKHHWb0HpusI0R9JQBdCCCF6wZiBOeRl+nDbvKSaMtGTO1+XweVvIn3wSmJGE8FEI/e98BkLV+/+CPQXX3zB/vvvz7///e+WYzNnzuSLL75g1KhRXarr5z84kF+dcTjpzkzSHdlEKwdRteJAjB3uTdMMUA0MyyQa7/87QwrRGySgCyGEEL1AURSmjC/B6/CDpRCqLNrlOYGCLbhzymhM1hKKhbn6L293ez66aZrcc889TJkyhY0bNwKQkZHByy+/zMMPP4zL5epWvVeeejA3/fQI0t2ZZLsKSDXmU754MpGGjK3PpYGiWIBJMmV06xpC7OskoAshhBC95MIT9sem2nFrXiIVgzB3kVcVBbKGLcfmCVEbr6SsJsS9L3za5etWVVVxwgkncMMNN2AYzRedPHkyixcv5rTTTuvOrbRy4YkTefj/TiIvLYsCbwlaKp3a5YdSuexgalaPwzJsODU3hdn+3b6WEPsiCehCCCFELxlZks0howpJc2ZiJl2Ea/J3eY5ms8geuRiDJI3xWl78YAVL11V2+ppz585lwoQJzJ07F2geyb/llluYN29eq52+d9f0g4fy6u9+wpiB+RR4S8hy5WM1FZGoHYhL8+KyeTjx0OE9dj0h9iUS0IUQQohe9PMfHIBTc+JQ3TSVD+lwecIdOX0RfIWlNOlBoskYtzz1AaZp7vScVCrFDTfcwPTp06mqqgIgPz+fd999l9/97nfYbF3em3CXBuan89qss7n9gqkMyS2g0FtMiW8oed4BTBpbzJlTx/b4NYXYF/T8d6sQQgghWhw1YRBDCjOJbIxQG4kRa8zAk9F2Ax/dMNlQ0QjAoIJ00kvWEKstoD5WzcqNTma/vYSLTprY7jU2bNjA2WefzRdffNFy7MQTT2T27Nnk5ub2yn1to2kqP522Hz85eiwrN9RQWtlIVsDNlPElsouoEN0kI+hCCCFEL1IUhQtOmIDX7sWmOAhuGdyp8zSbRcbQFSStOOFEiEf/t4BgON6m3LPPPst+++3XEs5tNhv3338/r7/+eq+H8x3ZbRoThuVz6pRRHLHfQAnnQuwGCehCCCFELzv9qDFkBjz47WkkG3NJhL0tr+mGiW6YGDtMYTHM5mPO9GqcGdU0JuuoD0V44F/bR8gbGxs599xzOe+882hqagJgyJAhfPrpp1x77bWoqvyKF+L7Sr57hRBCiF5mt2mcdcxY/M40VEWjcdOwltc2VDSyoaKRzVWhlmObq0ItxzOGfIuppGiM1/OveStYV1bPxx9/zP77789zzz3Xcs55553HokWLOOSQQ/bovQkhep4EdCGEEGIPuPjEiQS8LtIcWcTrCog2pnfqPKcnijd/A2G9kUg8yk8uvJKpU6e2rG2elpbGc889x9///ncCgUAv3oEQYk+Rh0SFEEKIPSDgc3HFKQdxz/OfEk4GaVg/Gtf+nzGoIB1ontaybRS9OC+AtsMUlYySdUTWByj75D9saihvOX7kkUfy97//nYEDB+7RexFC9C4ZQRdCCCH2kItOnMig/HQyXDnokTSaqgZg01RsmtoqkGuq2nLcsiwiS+pJzXsJY2s4VzWNu+66i/fff1/CuRD9kAR0IYQQYg/RNJWbzp2C2+bGrXkJbhiFnuz4j9lG1KDy2Uqq/1UNevOOoKovk2E/uI5f/PIaNE3bU00XQuxBEtCFEEKIPeiYA4YwZb+BZLpzQXdRXzoSAJumMqwok2FFmdg0lejaKJv+uInIskjLufbhg7AfeRaGt4B/zFm6t25BCNHLJKALIYQQe9idFx2N3+UmzZFFrLqYyA4PjFq6Re0btZQ/UY4R3Dpq7lHJPy+fvJ9kYmoq4WSI595fjq7vfHdRIcT3kwR0IYQQYg8bkBPgih8eRMCZjl110rBmPIaukqhIsPnPm2n8sBGs5rLuYW5KflWCb7wPVyCEI1BPU7KRyromXvt81V69DyFE75CALoQQQuwFl804iBFFWWS78zFiXsr+42DznzaTrEg2F9Ag6+QsCi8pxJa2fZ66f0ApKStBLBXl7+8s2UutF0L0JgnoQggh+p3qhjCfr9jMl99soawmhGlae7tJbaiqwoO/OAG3HoPPXyP59XJontGCI99B8S+KyTgqA0VVWp3nzapBc0VpSgVZsaGGirqmvdB6IURvknXQhRBC9Csvvr+cv/z3K8pqmtcUT/O5mDS2mItOnMjE4fkoirKLGvYMy7L48K2X2fjG3aRisZbjvsNyyZ3hQ7W3P4amKODOrCRS7se0LN6av5aLTpq4p5othNgDJKALIYToN1aUVvO7f3xEbaiBsB4ELBpibmo/a+KjJRs5/4QJXPnDg3E77Xu1nRUVFVxyySW8+eabLcds3iy0iceRyvNhWp+iond4viermnD5EOKpKO8vKpWALkQ/I1NchBBC9BsPv/olTbEYDalqTGc9SqCcsFlPVWwz5Y1VPPLqV/z8/teobYzutTb+61//Yty4ca3C+cUXX8K0y+4lv+hgrKSXmlUTdjotx5XWiGJLEtUjLFlbKau5CNHPSEAXQgjRL1iWxbL11URSTViKSf6Ez8nf70uKDpmHO6eMkF5HdaScT5dv5MJ7X6WyPrxH29fQ0MC5557LmWeeSX19PQB5eXm8/vrrPPnkE/z1+tPJ8vvIduWTbMyhYcPwDutSFHCm1ZMwYsSTOl+vLt9TtyGE2AMkoAshhOgXwrEk1Q0RUmYCm7sJzdG8GormSJAzagnZoxaTVMJUR8tYtr6Si+75L2W1oT3Stjlz5jB+/Hiee+65lmOnn346y5cv5+STTwagKDfAvZdPw+v0EbBnEi4bRv2mQR3W6fA1oltJLGDV5rpevgMhxJ4kAV0IIUS/oKBgWRaWZaHaUm1e9+ZUkjtuProaoTpWxsqNVVzxwBtE423L9pRIJMLMmTM5/vjjKSsrAyA9PZ1//vOfvPTSS2RnZ7cqf+wBQ/jFaYeQ4crCb8+gaeMoGjoI6TZ3FAsL3dTZWBXstXsQQux5EtCFEEL0C26nDUVRUBUV02h/DQRXWpC8cV9iaBFqYuWs2FDN7bPnYVk9vwzjRx99xIQJE3jkkUdajk2bNo1ly5ZxzjnndLiazC9+dCiXn3IQma5s/PZ0QhtHUbd+WJs56XZn88ovhpmiumHPTtcRQvQuCehCCCH6BU1T8XscaKqGmXR1WM4ZCJE7eiEpEtTFqnnlk2948f3lPdaOeDzOr371K4466ijWrVsHgNvt5i9/+QvvvPMORUVFu6zj2p9M4tIfHEimK4c0R/N0l6qVB5BKbn/jYZoaAIqi4nbt3VVphBA9S5ZZFEII0W+U5KVT3lBDU8JBKuHA7ky2W86V3kBaySqCG0fSFHfz++c/ZdyQPMYNzt2t63/00Uf88pe/pKqqquXY5MmTefrppxkxYkSX6rru7Ml43Q7++O8vsKtO6hpUKhel4S9aiy+vjHgoHVCwqTbSPM7darcQom+REXQhhBD9xrhBObhsHgDiwfSdlk0rLsWVUU1Dsob6piaueeQdQpFEt64biUT4v//7P4477riWcO52u/njH//Ihx9+2OVwvs2Vpx7Mn//vRPLTsyj0DsRhZBFcP46yz4+naeMo3JoXTdGYMWlkt+oXQvRNXQ7oH330ETNmzKCwsBBFUXj11VdbXkulUlx//fWMHz8er9dLYWEhP/vZzygvl+WfhBBC9L6DRxViU22oio1EKGOnZRUFckYuQ3VGqI1Xsrasjluffr/L89HnzZvHfvvtx5///OeWY5MnT2bJkiVcffXVaJrWrXvZ5oRDhvHG3edw+NiB5HkHUOgdSIYzlwxnLtmefA4bU8R+Q/N26xpCiL6lywE9EokwYcIEHn744TavRaNRFi5cyK233srChQt5+eWXWb16NaecckqPNFYIIYTYmcnjSlBVBZfmJlaXv9PNfgBUe4qcUYvQSVAfreat+WuZt3hDp64VDoe56qqrOProo1m/fj3QPGp+8cUX89577zF8eMfrmHdVQZaf5275MS/edjonHTKaQ4YNZWxRCRefeABP/Vp+xwrR33R5DvqJJ57IiSee2O5raWlpzJ07t9WxP//5zxxyyCFs2rSJkpKS7rVSCCGE6ISsNA8Hjizk4+VRotEmog1Z+LLqd3qOMxAibeBqghtGEk2m8fvnPmHyuGIc9o5/RX7wwQdcfPHFlJaWthw74ogjePzxx1m9ejWq2jszSA8YUcAjI07ulbqFEH1Hrz8kGgwGURSF9PT0dl9PJBIkEtvn/IVCzZtGpFIpUqmeWZt2Wz09VZ/oOdI3fZf0Td8lfbNzPz5iFF9+U4ZNcdBUWYI3s+0mPqZlUVreCMDgwnQChaVEKotoSNSwtszFY//7iitOOajNeeFwmJtuuonHHnus5Zjb7WbWrFlceeWVGIbB6tWrpW/6IPm+6bv2pb7p7D0q1m4s/qooCq+88gqnnnpqu6/H43GmTJnCqFGjePbZZ9stc/vtt3PHHXe0Of7cc8/h8Xi62zQhhBD7KMO0+PULq6mJNhKhkczxb6LZWz/8aVpQHWxe4SU3zYGqQCKUS2jNFLykk+NN4/YfDcG/w/KFS5cu5eGHH6a6urrl2NixY7nqqqsoKCjYMzcnhPhei0ajnHPOOQSDQQKBQIflem0EPZVKcdZZZ2GaZqtNGr7rxhtv5Jprrmn5PBQKUVxczPTp03fa8K62Ze7cuUybNg27XdaK7Uukb/ou6Zu+S/pm1xbW+3nuvaXEwmGM0DACJRuA5pFzAMOwYGtAd7ncaJqC2xMmVV9DosGBqeawNprJzT86goaGBm644QaeeeaZlvo9Hg+zZs3iiiuuaDWdRfqm75K+6bv2pb7ZNlNkV3oloKdSKc4880xKS0t5//33dxq0nU4nTmfb9VvtdnuPd1Jv1Cl6hvRN3yV903dJ33TsghMm8uIHK3FrXqLVJaQXb0BVFUrLGtqU3VQVbPnvkkGrqWjII5Ro4OVPVlFobeE3N19PZWVlS5kjjzySp59+mqFDh3Z4fembvkv6pu/aF/qms/fX4wF9Wzhfs2YNH3zwAVlZWT19CSGEEGKnhg3IZPzgXL5cHaU6FiZcm0sgt2aX5zl8ETw5ZYQ2R4l99QqXPb2s5TW/388999zDZZdd1msPgQohBHQjoIfDYdauXdvyeWlpKYsXLyYzM5PCwkJOP/10Fi5cyOuvv45hGC2jDpmZmTgcjp5ruRBCCLETP//BASz7UxUO1U1o00h82dW7PMeyLLSa+aQ+qCWlb9+FdMaMGTzyyCMUFRX1ZpOFEALoRkBfsGABRx99dMvn2+aPn3/++dx+++3873//A2D//fdvdd4HH3zA1KlTu99SIYQQogtOOGQYYwblEF8XpyoaI1Q5gCGFza8ZpsnGyuapLQPz09BUlVRtivLHy4mtj7XUoTp9/N/1t/PA7degKMreuA0hxD6oywF96tSpO91lbTcWhRFCCCF6jKIo/PrsKVzw+1dxa16aNo/Al1uJzWZiWjuEbROCHzdSP7ceS9/+O0wpGkXuAWdQqQ2UcC6E2KNkEp0QQoh+a/K4Yg4bU0SGOwcz6aZx0xAA1G2Bu1qn4pEy6t6qawnntgwbBRcV4jjkSKKqzsI1FZRWtH24VAgheosEdCGEEP3aHRdMxWN3EXCkEykfQjziBsMifakJL4VIlm+da65A2hFplFxbgneUB0/uZuJGhJRh8M+5y3Z+ESGE6EES0IUQQvRrQwozOOe48aQ7s9BwUPNxDpse2EzjvEYwm8s48h0UzSwiZ0YOqqP5V6M/fwsWJuFEiDe/XINhmHvvJoQQ+xQJ6EIIIfq9a888nHSngbpkHon330ev27rdtgaZ0zMp/r9iXCWuVuc4PDEcgQaiRpiahgirt9TthZYLIfZFvbaTqBBCCNEXmKbJP/72DKv/81uioe2bEtkH+Ck4KwNHXsdLADvTagmHsrCAz1dsYfTAnD3QYiHEvk4CuhBCiH5r2bJlXH755Xz22Wctx1SHB/uYIzEHlWD5PwPiHZ7vCjTShElST7B4bWWH5YQQoidJQBdCCLFblqyt5P4XP+ObTbWkdJPRA7OZcfgITjtiNB7X3tm2OxqN8tvf/pY//OEP6Lrecvy8887DGHwcX6ytpzy8idpv9yd/wnw0rf0lgp3+RgASRpx15fV7oulCCCEBXQghRPctXF3OT+96hUg8RjgVAizqwo0sWFXOH176nDsunMqMSSP3aJvefPNNZs6cyYYNG1qOjRgxgkcffZRjjjmGUCTOD256npRRQGVEp3bNGHJGLEdV2651rtkNVHsS3UxS3Rjdg3chhNiXyUOiQgghuiWlG/y/R+fSFItQEd1E2KwlbNVQHSujLFxKZbCOax6Zw61PvY9p9v4mduXl5ZxxxhmcfPLJLeHc4XBw++23s2TJEo455hgAAl4Xj1x9Mn6XlyxXLvGaEmpWj+uwjYqWwsQikdTbfV0IIXqajKALIYToliXrqthcHaQhXovmClMw8VMU1SAezCBYPojaep24EeX59y0q6sM8cvXJOOxaj7fDMAweffRRbrrpJpqamlqOH3PMMTz66KOMGDGizTnjBudy98+P4dePvwso1NVAtamRM2IZmu07QV2xsLBIGSaWZcmuokKIXicj6EIIIbrloyUbMEyTpBXHl1eGZjNRVQVPRiN5oxcRGLycsN5IdbSMeYtLueje//b4SPrChQs57LDD+MUvftESznNycvj73//Ou+++22443+aUyaP4wxXTSXelke3OJ1k3gIqlhxFt8mBZze00DQUj7sGu2slN90o4F0LsERLQhRBCdMuqzXUkjQRg4UprvUa4qipkFG0ha9RXxK0mqiJlfLFyC/e98GmPXLu+vp4rr7ySgw46iAULFrQcv+SSS/j2228577zzOhWmTz58BH/+5UlkeTPI8xajxHKoWTKF6tVjCdVmUbd+BFgqbpuXoQMyeqTtQgixKxLQhRBCdIsFWDSPNCua0W4ZX3Y9WaMXkLCiNMRrefLNRby7YF23r2maJk8//TQjR47k0UcfbRnpHjNmDB9//DFPPPEEmZmZXarzuAOH8MJtP2bUgHwKvSWkOXJI1Qyh4ZuDiVYOxm9Px2lzcdmMg7rdbiGE6AoJ6EIIIbrFZbehbv01YukdL6foy2zAX7yKplQDkVQT1z3+Lpurgx2W78jChQuZNGkSF198MbW1tQB4vV7uu+8+Fi1axJQpU7p3I8DYQbm8fvc5/PzkAxmQls8A32AKfYMY4BtMljuXnx43nkNHD+h2/UII0RXykKgQQohuyU33YlObf43oCddOy6YXl5JsyqCuQcWhOrn8gdd55Xdndeqh0YaGBm655ZZWI+YAZ511Fvfffz8DBvRMcHbYNa4/ZwpXnXYIr322mvUVDeimyQmHDOOQURLOhRB7jgR0IYQQ3TIwPw1V1VBQScW8Oy2rqgrZI5dSschPTayCVZvt/OXVr/jVGYd1eI5pmsyePZvrr7++ZcQcYPTo0Tz88MMtyyb2NK/bwVnHjuuVuoUQojNkiosQQohuGVmchaoo2BUn8WDWLsvb7AZZIxeRsuKEEg0889YiajvY/GfhwoVMnjy5zXSWe++9l8WLF/daOBdCiL5AAroQQohumTA0n9wMH26bl2RTBkbS2aaMbpis3VLP2i316IaJJ60Jd85mgsl6wvEEdz33cavyDQ0NzJw5k4MPPpgvvvii5fhPfvITvv32W6677jocDkev35sQQuxNEtCFEEJ0i9NhY/L4Yrx2H1gK4Zq8Tp2XMXANaCkaE7W8+cUaNlY2tqzOMmLECB555BFM0wRg1KhRvPvuu7zwwgsUFRX15u0IIUSfIQFdCCFEt510yDBsmh274iRWl99yXDdMdMPE2Bq0AQyz+ZhiT+AtWE8kFSKpp7jh/tkcdthhbaaz3HPPPSxZsoRjjz12j9+XEELsTfKQqBBCiG47fGwxuelegjEvwVAmRtKB5kiyoaKxTdnNVaGW/x40YCPh9bmUffI0L2xe3qrcGWecwR/+8AeKi4t7u/lCCNEnyQi6EEKIbnM6bEwaV4zX4QdLIVTRiVCtW4Q+qSb13nMkdwjnY8eOZe7cubz00ksSzoUQ+zQZQRdCCLFbfnLMOP736Srcqo+m8kGkDdjIoIJ0oHlay7aR86JcP4lv4zS8UUd9g95yvmJ3s9+xZ7Hgtb9is8mvJSGEkBF0IYQQu+WgEQVMGltMmjMDS3cQLBuITVOxaSqauvXXTJ1O7TPV1Dxbhb4tnCugDh2Fb9qlRLMmUh+K772bEEKIPkQCuhBCiN2iKApXnnowLrureRS9bAh6wg6AETVgXgSeCxFfF2s5xz3UTfHVxQSmDSahWZiWxX8/W7W3bkEIIfoUCehCCCF228GjCpm6/yAyXNlg2GkoHUbwsyBlf9gMSxNgNZezZdjIPy+fwksLcRY48eVUYGES0yO889W6vXsTQgjRR8hkPyGEELtNURSuO2sSn6/cTH1ZA8F5n0FT3fbX7QoZx2aQfkQ6qn372JDD24TqjBFNhVmxoQbTtFBVZW/cghBC9BkS0IUQQvQII1xDctGzNC3+vNVx30Qf2SdlY0tr+ytHVRVsnhB6MBNdNyirDVGcm7anmiyEEH2STHERQgixW2pqarjqqqsYN24cq3cI50paLq5px5P3k4J2w/k2dlcU3Wp+cHTNlroOywkhxL5CRtCFEEJ0Szwe509/+hOzZs0iFNq+CVF+QQHuUScQyxxKXbKK+vUOsoZ902E9qj2JaRkANIYTvd5uIYTo67oc0D/66CPuu+8+vv76ayoqKnjllVc49dRTW163LIs77riDv/71rzQ0NHDooYfyl7/8hbFjx/Zku4UQPeysv35OVWiHcGRZhCMaD67+BJTtc4LzAk5euPTwvdBC0VdYlsVLL73EDTfcwIYNG1qOe71err/+eq699lo+Xl7OLx9+m5SZJFRhYXdHCAzY1G59impgbX2KNJpI7olbEEKIPq3LU1wikQgTJkzg4Ycfbvf1e++9lwceeICHH36Yr776ivz8fKZNm0ZTU9NuN1YI0XuqQglKayPbP+qi1MQVSuuirY63CvFij7MsiwWryvngm3qefHMRS9dVYprWHrv+559/zqRJkzjrrLNawrmqqlxyySWsWbOGW2+9FY/Hw/GHDOOiE/cn3Z2FW/XTsH4MDRuGYbXTVD3mQ1Oax4syA549di9CCNFXdXkE/cQTT+TEE09s9zXLsnjwwQe5+eab+dGPfgTA3/72N/Ly8njuuee47LLLdq+1QgixD9tQ0ci1j85hybpKIpEInqUhHnjpCwJeJ6dMGsn150zB5eidmYulpaXccMMNvPTSS62OT5s2jfvvv5/99tuvzTlXn34YZbVNvPEF1Ec1QpuHkYwEyBmxDNWeAsCyINGYg0N1oaoKh4wc0CvtF0KI75Me/UleWlpKZWUl06dPbznmdDo56qij+OyzzySgCyFEN1U3hLn0D6+xeks1dbFq4kYEJaziUJ00Jrz8Y26c9xaV8tBVJzBxeEGPXbexsZFZs2bxpz/9iWRy+/STMWPGcP/993PCCSegKO0vi+iw2/jDlceT6Xfzj7lLscXtBOtVtnyVhSe7AldaHbHGLIyEG6/Lz5DCDLLTZQRdCCF6NKBXVlYCkJeX1+p4Xl4eGzdubPecRCJBIrH9T+bbHjRKpVKkUqkeade2enqqPtFzpG/6kPbmHnRQTvprz3vk1a9Ys6WW6mg5hi2MK28VDqeNRCiTYGMO4VSIhJ7HuXe+zM0/ncyZU3fvuZ9kMskTTzzBnXfeSV3d9pVVcnNz+c1vfsOFF16IzWZD1/Vd1nXD2ZMYkOPnT//5ElfETSjRSKzKSbiqCAUFv5aOx+7lkpMmfu//bcnPtL5L+qbv2pf6prP32Ct/C/3uaIplWR2OsNx9993ccccdbY7PmTMHj6dnR1Lmzp3bo/WJniN9s/eFIxqw6w1iwpEIb775Zu83SLSIxHX+9V4p9eEGksRJH/wpdl9zaHZkQirmp2njgVREkjTF0rnuL2+xasVSDhzc9fXETdPkk08+4Z///CdVVVUtx+12O6eccgo//vGP8Xg8zJkzp0v15gAXT8rgvwtTrK3y47K8mKaBoqjYFI3DBjmxNa7lzTfXdrnNfZH8TOu7pG/6rn2hb6LRaKfK9WhAz8/PB5pH0gsKtv+Jtbq6us2o+jY33ngj11xzTcvnoVCI4uJipk+fTiAQ6JF2pVIp5s6dy7Rp07Db7T1Sp+gZ0jd9x4OrP6EmvusfHD6vl5NOmrIHWiS2mbNgHXFzM7qaxOVrIi03RjQKHo+nefDDaxLI+Iq6dWOJVCu4HW5eWRrmJ6dMZ0RxVqev8+6773LTTTexePHiVsfPOuss7rzzTkpKSnb7Xi4/z2JzTZC3v1pPZV0Yj8vOtIMGs//Q/N2uuy+Qn2l9l/RN37Uv9c2OS9LuTI8G9MGDB5Ofn8/cuXOZOHEi0Pxn0g8//JB77rmn3XOcTidOp7PNcbvd3uOd1Bt1ip4hfdMHdPBXrvbKSV/tWTXBGKZpYaDjy6ht+Yukoigt/63ZIHv4CqoNG/V1Kg7Nwcw/vc1/7zyLNJ9rp/V//fXX3HDDDbz77rutjh933HHcc889HHDAAT16P8OKcriqKKdH6+xr5Gda3yV903ftC33T2fvr8jKL4XCYxYsXt4ywlJaWsnjxYjZt2oSiKFx99dXcddddvPLKKyxfvpwLLrgAj8fDOeec09VLCSGEAJqiKcDCwkTVOp7zraoK2SOWoXoaqY5WsKm6kZkPvYnVwfMF69at4+yzz+aggw5qFc4nTpzInDlzmDt3bo+HcyGEELvW5RH0BQsWcPTRR7d8vm16yvnnn8/s2bP59a9/TSwW48orr2zZqGjOnDn4/f6ea7UQQuxDNHWHv25YOx9XsdksckYvpGrJJGpiFcxfqfLfT1dx6pRRLWWqq6v53e9+x2OPPdbqIc8hQ4Ywa9YszjzzTFS1y+M3QgghekiXA/rUqVM7HI2B5j+53n777dx+++270y4hxB6WF/jOVDPLIhyJ4PN62+wkKvYsn9sBKCiomPqu/zzq9MRJH7aUhm8PIqJHeOClzznp0OEkEzEeeOAB7rvvPsLhcEv57OxsbrvtNi677DIcDkcv3okQQojO6J0dLYQQ3zsvXHp4q89TqRRvvvkmJ500pd/PCezrBheko6oqNsVOPJTR5nXdMNlQ0QjAoIJ0bJqKL6uGcKCWxiYHZTUuLvnVrbzzr6eorq5uOc/r9XLttddy7bXX9thD+UIIIXafBHQhhOjjhg3IZEB2gMZoHeFwGmZq12+YVFUhUPItNW/VsnHNM6yPNLS8ZrPZuPTSS7n11ltbVt8SQgjRd0hAF0KIPi47zcPwokzWlVfRlGwgHsoCVyOGYYKiYJhmS1nDNLEsi+iKCI1zN2JUt94U48wzz+TOO+9k+PDhe/o2hBBCdJIEdCGE6OPsNo0Dhhfw3tfrULERb8jCWbCODZXB1gUti83za+HzGNQYrV5y5Q3ntPOv4rl7/m8PtlwIIUR3SEAXQojvgcPHFuN02HHG3URrC7Hn2oDk9gJlqeZgXt56GUZniQu96Hj8hRPZHPPvdGdnIYQQfYOsoyWEEN8DwwZkctDIQnz2AKZuJ1EzhEH5aRToLlxvRuE/Ta3CuaPQQcGFBRTNHIBzsIe4HqWyPszm6s7tYieEEGLvkRF0IYT4Hgh4nZxx1Bi+WLkFZ8pNZE02qY8XEv0m3KqcPcdO1vFZeMd5Ubaun+5MqyXSlINlWby/cD0XnDhxb9yCEEKITpKALoQQ3xNHThjEyGyV8k/eQd+8hFaTWQIqHOqmcGoudrvW6jxXeh3hzSZJI8GitZVcsCcbLYQQosskoAshxPdAaWkps2bN4p3ZszGN7Q+Aan47mcelEzg4gGJrf2653ZkAwLB0mqLJdssIIYToOySgCyFEH1ZaWspdd93F7Nmz0fXtY+aKw4M27GC0EUPxHvAlii3eYR2q2hzoTcskntQ7LCeEEKJvkIAuhBA7YZoWqrrnVz3pKJinpaVx3kWX8nF1OjUxlbpUJbXfHEDe+C9QNLPdugyj+Ue9qqi4nPJjXwgh+jr5SS1EN1iWRTSeIhhJEIomiCVS6IaJYVoYhomiKDjtGk6HDaddw+O0k+F343HtegdIsXcZhsnGqkZWbqhhY1UQn9tBQZaPzICHQfnpZKd5evX6Owvmv/rVr/jlL3+J1+vlvr++yCtLo+g1Og1NJnWrJ5A1Ykm7IT0V8QNgU+ykeZ292n4hhBC7TwK6EJ2UTBlU1DVRWR+mLhRr2b0xkUySTCQxTAPDMDBNE1VRsNvt2O12bHY7dlvzt5rLYSPd5yIr4KEw24/LId+CfUkiqfPX17/mX/NWsrm6EWPrXG+Xw8bQwkx+MHkUE4bmM2FoHn5PzwbdzgTz9PR0AFKpFKMH+CgeNpZZ//wUI6TTVAupuJvsUYuxu6Ot6g5XFmNTHDg0B1MnDOrRdgshhOh5kg6E2IWGphjryhuoqg9jmCZNTU00BoNEIxGi0Ri6ntplHTabHZ/Pi8/n2/rhZ8WGarLTPAzIDlCQ5cNu03ZZj+g9pmlxx98+5MUPltMUDxI1wpjoqGhoSTuNa5pYVlrJ4WNLOPvYCRw2pojCbP9uX7crwXxHqqJw6pRR1IXiPP7619ia7DSGNSoWTsFfsAl3Ri2aM0ZTdQGJxlwyHOlkBNycfNjw3W6zEEKI3iUBXYgOhCIJvt1US1VDmFgsRnV1NXV19eh6CrtNxefUyAtoeBwOXHYVTVVQFQVVBcsC3bBI6iYpwyKaNAjHI1SEghimhWazkZGeQTAri5rGCMvWq5TkpTFsQCZup0yD2RtenLeCl+atoD5aQ8QM4vCHcPuCGEkXyaY04iknzpSHT5YarN1Sx5WnHca0g4YyKD+9W9frbjDfkcth4/IfHkxBlp8//vsLymscBJMNNJUNJVQ2qKWcV0vD70zjZ9MnYJM3gkII0edJQBfiO1K6wbL11ZTVhojHE2zZsoX6+jrsmkq2306m14fPtYtvHQU0VcFpb96sN5Pm0G1ZFrGkSX0kRV2wntraGux2Ozk5OSRSKTZWBSnOCTBsQCZet6O3b1VspesGT7+xkGgyTMQMklayhrSSdShbnw21TIVwVTHBDSNpNBIYdTp//s/neFwO0rxOMvzuTl9r7dq1/P73v+dvf/tbm2B+9dVXc/XVV+8ymO/I5bBxxtSxjCjO4i+vfsW8xRvQdZ2EHsfCxK45cTmcnHHUWGaeenCn6xVCCLH3SEAXYgd1wSgL11QQjibYvHkTtbW12DWFwTkesvx2VGX3VvNQFAWPU8Pj1CjKdBGO69SFU1RWVFBZWUVubg6JRAGba0IMzk9nZEk2Nk3tobsTHXnnq3VsqGwkmGzA5gm3CucAimptnTZSQ+03B9AUsVAbVB57dT7pPifTDxq6yylKy5cv5+677+aFF17ANLc/yNndYL4jVVWYOLyAB648nmXrq/hsxWaWrqsikTLITvfw4yNGc/TEwSi7+e9XCCHEniEBXQiaR7ZXba5jzZY6QqEQ69avx9RTFGe5yA04djuYd8TnsuFz2SjMcFIVTFJVXUVVdTV5eXnohkF5XRNjB+X2yFxn0bEFq8pJmTopK07mgFI66m6bK0bO2K+oWjKJUEJlXbnKY/9bQJbfw2Fji9qve8ECZs2axauvvtrqeE8E8+8KeJ1MHl/C5PElpHQDVVHQ5A2eEEJ870hAF/s807RYtKaCstoQW7aUUVlZgd+lMaTAj8O2Z8KNXVMpynRRkO6kMpigvLKS+rp6Bg4sIZ7U2VTtZcLQPJmf3ks214RIGc07bDp8wZ2W1RxJcsYsoGrp4YSMehat0nj5428oyg1QlBNoKffRRx8xa9Ys5syZ0+r87OxsfvWrXzFz5kzS0tJ6/ma2koeOhRDi+0sCutinGYbJ16srqKhrYt26tTQ2NjIgw0lBunOvTAfQVIUBGS6yfQ421sZYs2YN6enpJAYNojEcZ/9h+eRn+vZ4u/q7pmjzMpkAmn3Xq/LYvWGyRy2iesXBRPUm3vj8W46eOIjCLB9z585l1qxZfPzxx63OKSws5LrrruPnP/85Xq+3V+5DCCFE/yABXeyzDMPky2/LqGoIs2bNGppCIYbne0j37P1RaqddZUSBl4ZIig21IZYvX86QwYP5SjcYUpDB6IE5e2V3y/6qeU17C6Dd6S26YbKhohGAQQXp2DQVV0Yt3pxyojUqDU0e/vT4bG68/C2WLF7U6tzBgwdz/fXXc8EFF+B0yiZBQgghdk0CuthnLVlXRVVDmFWrVhGLhBlZ4CXg7lvfEhleO36XjdKaKGvWrCEvLw/TtGgMxzl41AAcdpnG0BOy0zzY1OY3ZsmoB7cj0anzAkWrCC0OUbX6Od5uqmn12qhRo7jppps4++yzsdn61r8rIYQQfZv81hD7pHVl9ZTVhihdX0o0HGZUoXfXSyfuJTZNYXi+l6pggk3V1USiUYYPG8YnywwOG1OEx7X3R/y7IxxLsqGykcZwnERSR9NUMv1ustM8FGT59ugUo7GDcpnz1VoUVBKhDNzpDUDzyDnQsmvstv82UybhhWGaPg5i1C1vVdeECftzyy0386Mf/QhVlQc0hRBCdF3fTCRC9KLqhggrN9ZQXl5OfX0dw/L6bjjfUV6aE69TY01VhJUrVzJy5Cg+WbaJw8YUEfB+f6ZOpHSDJeuqqKhrIpVK0RgMkkomsdnsVPt9uN1u/B4nYwflkJO+Z+Zq7z80D1VVsSl2EqH0luPbprW0iJtsfr0KFschZrV6yZZZzOEn/pQXH7qRgixZdUcIIUT39f1UIkQPSqYMFq2poLGxkS1btjAg00Wm7/szAu1z2RhT6GNVRXNIHzFyBJ8uNzlk1ACy0jx7u3m7FIkl+fLbMhqbYmzatIm6+jos08SmqRimhWVZeL0+SkpKaIomGFWSzfCirF5v17CiTHxuB/aIk3hTBpapoKg7BPAmAxbFYUUCvvMMqXuYGz1vOp7MscT9g4jGd/2QqRBCCLEzEtDFPmXFhmoi8QTr15eS4bVTmP79GXnexmlXGT3Ay5rKKKu+/ZZhw4bzxUqLQ8cUkd2HQ3oyZfDZis00hMKsXr0aI5WkKMNJjt+BTVMwTIumuE5ZfZxvvllJYWFhy3ljB+f2atsy/W6GFmZQ3dhANBkiWpuHN7eSQsVD8KNGIkvCYO5wggKe8V4yp2bgKnJRudSHHkpR2xihvLaJoQMye7W9Qggh+jcJ6GKfUdMYYUtNiM2bNmOZOoOy/d/bnRXtmsrIAi/rqqKsXrOa4cOH8+U3CoePLdrptvOGYRJL6sS3fqR0A4/Tjs/twOt29Fp7Lcti8dpKmqJxvv32W2wYjBrgw2nfPkdbUxXSPXbS3DYqGhNsKS9H15uXPnQ77QwpzOi19jkdNk6ZPIpFayqwJR00LPISLCsn+m20dUEN/AcHyDwqA3vW9r+8OP2NhIPZWJbF0vVVHDFhYK+1VQghRP8nAV3sEwzDZOm6KoLBELW1NQzO8WDfQ5sQ9RZNVRiW72FdVZS1a9aijRzJ/G/KmDS2uM2c9LpglI1VQSrqmjCt7VM3TNNqWa7R5bBRkOVn+IBMnI6e/dGwuTpEVUOYtWvXsaUmTFI3WbKpuS35aU5GFXopynShKgqKolCY4cKuqZRWV+F0Nq9JnxVwk+Zz9Wi7dnTsxIHc//B6Up++gt6wpdVrqlvFHO+A/VxkDc3E9p3dOR2eMCYGpmlQUR/utTYKIYTYN0hAF/uEjVVBIvEkGzZuwO+2kRPovdHiPUlVFIbmeVhdEWH16lWMGjWaL1ZuYfK4YrxuB1tqQqzeXEckniQeT1BTU0M4HCaZSpJMJrFME7vDgcftIRAIEI7msKkqyJDCDEpyemZDJNO0WLW5lrUby3j2gzWEEwYWBrqlgwIOxcHbS1UGZDiZMTGXEQXND4bmBBzEUwZbyrYQCARYvLaSIycM7PG/esTjcZ599lnuu+8+Vq9e3eo1Ld1OxpFpBA4OoDp39oZOafl/Tft+v/ETQgix90lAF/2eaVqsK6+ntq6ORDzO8KL+tcKGqjQvw7iqIsKqVasYPWY0nyzbRMDr5NtNtazfXEVFVQ3xeIyCdAcDMtz4XAp2nxNNVUikTMLxCFu2BCmvKKcgP5+krlNaXk8saex2+8pqQ6wtq+fhVxcSSyWI0EjCaL3OuFNzkqhL47H3Exw0OMDph+TjsKkMyHQRjOps3LgBr9dDeW0TA3ICu90mgOrqah599FEeeeQRqqurW71mS8uHIRNwjcoibb8FKJrZQS3NjJQdBRVFUUjzfP+eaxBCCNG39HhA13Wd22+/nX/+859UVlZSUFDABRdcwC233CJrAou9YlN1kFgiRXl5ORleOx5n/9vcR1MVRuR7+aY8zFeLV1AecbB6Sz2VdUEMXUdVFeyagqYqFGe5GVfk44iRGbgd278WKd2kvDFBWVkZVdXVDB0yhNXlERrDcXIyur/Szdot9Tz9xtc0JaI0WXVo7ghZJaux+4JgKSRCmYQrSqiOJPBoHr5cb1IdSnLJ1CJ8LhvFWS5WVYRpDAZZvcVB4W4+O7BixQr++Mc/8uyzz5JItH6jcPTRRzN1xjm8vCJFeW0twXANdWv2I2vk4nZ3GN0mGfGjoqGqKiW5ad1umxBCCAG9ENDvueceHnvsMf72t78xduxYFixYwIUXXkhaWhq//OUve/pyQuyUaVqs2VJHXV09iXicYf1s9HxHNk1BN0ye/2QL0aSBQQJdjWGpOpZpopgKLtVFrMbNproon69p5CeHFTCqsHlKid2mMjDbTX6ak7VVUVatWkU4EuWLlWVMGlfSrWUcU7rBCx+soLIhRJPVgM0XJHfcfFSb3lLG7ongzdtMtLqIhvVjSCVTWLU5PDFvCzOPKyHNY8fnslG2pYz0tDSqGiLkZ3Zt+o1lWcyZM4c//vGPvPPOO61e0zSN008/nWuvvZaDDz6YeFKncO5S7nvhE4wmnXAtqLYUGUO+QVHbjqTrCRfR2gI8qge308HYwTld/joJIYQQO+rxgP7555/zwx/+kJNPPhmAQYMG8fzzz7NgwYKevpQQu1TVECae1KmoKCfdY8fbD0fPt/no23penF9JNBmjyWrAUkzsrjCerGrszhSm7iDWkEM0HEBTNJJmJn/9YDOTR6Rz2kF5qFuHiJ12lVGFXr4pC7FqSxn1DY0sWGVj6v6Duvzw6JaaEJ+v3Ew4FcJUUmSNXNQqnG+jKODN24LdF6R2xcHUJEGpVXj203IuOHIABelO1lSGiUajlNWEOh3QY7EY//znP3nwwQdZsWJFq9cCgQCXXnopv/jFLygpKWk57nLY+OHkkdSFojz66nysuEm4soRkUwbpQ1biSqtvKWuZKvVrx4Gp4XOmcdSEgQwtlCUWhRBC7J4eD+hTpkzhscceY/Xq1YwYMYIlS5bwySef8OCDD/b0pYTYpc3VIcKRCLFYjJKC3t2VMmWYbKmPs6EmxoaaGBWNCQzLwrLApip4XRo+p42B2W7GFvnIT3P02AOP876p4/nPK4nqYSIEUT0NOAsX4UoPYrNpuB12VFUhbeBqUjEPDevGUtNo4LP5+GSVhWnB6QfntbRHUxWG53lY9a3JuvXr8Af8LCut5qCRhV1q15yv1hGJJoiZETy5Fdjd0Z2Wd3ibyB77FdVLD6MuVceyzQqfrm5g8ogMbJpKXV09fp8PwzB3+jBmVVUVjzzyCI888gi1tbWtXhs8eDBXX301F154IX5/+39RyUn3ctqU0URiSf45dwm2mINwxE71skNxeEPYvU0oqkG8MRs95iGgZRLwejjn2HE47P33TaAQQog9o8cD+vXXX08wGGTUqFFomoZhGMyaNYuzzz673fKJRKLVPNBQKARAKpUileqZHfm21dNT9Yme05t9k0jqlNcGqaqsRFUsPPbmZyR6UsowWVDaxNcbQmypT2CYFqZlkrSSpMwUFs1LGiooqIqKpmgs3ezgjcUqGV4bYwq9jBngY2iuG03tXlhfXx3lpfmVRPUmwlYQR8ZmAoO+Rrd0dL15GcVESse1dfTb5oqQPeZLIpUlNJaOxbRMPlsNHrvC8eN32LXTMsnzWph6ivXr1qMwlNw0NwVZnZ9e8vXqchJGAgMdT84WrB2WeOyI3RMia+RCalceQlgN88YildEFHgIuhZqaGgoKCiirCbbbjmXLlvGnP/2J559/nmQy2eq1yZMn88tf/pIZM2agac0hemf/7gbnB/jpceMpyPTx9zmL2VTpIG5ESEXcJCJZWFho2EnX/KR5A1w240AOGJ63R37OyM+0vkv6pu+Svum79qW+6ew9KlZnfmN2wQsvvMB1113Hfffdx9ixY1m8eDFXX301DzzwAOeff36b8rfffjt33HFHm+PPPfccHk/f3RVR9H2VwQQba2KsL11Pml0nuwf/ORkmrGlQWFKlEUlBkiQpJUWKFAYGFhaKaqCoOigWmBqm0fygpYKCHTsOy4EDByoqmW6LwwpN8n1d+3ZM6PCvb200JHQiWiO29FI8RV+gKGAButl8PZvNhm3rQ6Ktzq8vpmnDwbjx4LU8HFlsMCyzdRuaElAZUSgoKCAjLcB+Jf5Ov5n4zX/WUtpQT8RqJHv//6FonX+DFN40kWTtUNKtdAanKRxaaFARVhg8eDDF2T6Ks5rXRDcMg6+//po33niDJUuWtKpDVVUmT57MjBkzGDFiRKevvaOmuM7aqigrysIs2RCkMZJqWUteVVWKs9xMHpHBpOHprR66FUIIIb4rGo1yzjnnEAwGCQQ6XpWsxwN6cXExN9xwAzNnzmw5duedd/Lss8/y7bfftinf3gh6cXExtbW1O214V6RSKebOncu0adOw27u/GoXoeb3ZN58s20Tp5grWrl3HuCJvj4Qnw7T4an2I91bW0xBNETNihPQQuqVjc0dw+Btw+BtwBhqwucOtVv6wLAU97ibekEu8IZdEMAssBYfqIM2WjlN1sH+Jn5P3zybd07k/bs3+uJz56xppMKrBVU/G6A9Q1O1LI5qWRUq3sNlsaDYbboetZWOibZrKBxEsHUOGPYMsl59rTxxIuseGYRgsWrSIiRMnsr42QTSlsN+ECYwblMvggvRdf60Mk0NnPs2m+jJiWhVFh3zQqXtqaXvKTuWiI3Ga6WTZs/jppHySusXQoUMZPmgAowq9PPPMMzz++OOUlpa2OjctLY2LL76YmTNnUlxc3KXrttsW06K8romNVUFqg1Eq6sIYpsWAbD8jijMZVpi5R6e2yM+0vkv6pu+Svum79qW+CYVCZGdn7zKg9/gUl2g02mY5RU3TMM321xF2Op04nW3XDbbb7T3eSb1Rp+gZPd03iaROOK4TamrC77bj74G1qaMJg799Us7qighRM0ZID6KbOq7MarKK1+LwB79zRusgrCjg8MRweDYSGLARU7cRb8gmVDaUmnASr83Lwk0m31REmD4+m6mjM1se3GzPhpooX29oImyEMNQkGUPno2pmq+tqioKlmeiGgaqpJHUDl8PWau57YMBGUpE0gjUq7pSb1xfXccGRA7bXoWkMzPGyfHMToWCQzTVuhhdn73L+vIWBbphYWKg2faflTdNifXkDAEMKM1BVBc2hkzHkG+pW7U/ClmT++iYmj0hn3Zpv+NfsP/PRnNeIxWKt6hkyZEjL/HKfr2c2WtpmcGEWgwuzME2LWCKF3aZht6k9vnFSV8jPtL5L+qbvkr7pu/aFvuns/fV4QJ8xYwazZs2ipKSEsWPHsmjRIh544AEuuuiinr6UEB2qCTY/jBgKBsnx7f43e2UwwdPztlDVFKcuVUfCSODKrCGreE07wbxzVJuOJ6cSd3YlkapightHEk1ESTPSeG2hSXlDgrMPL2h3OolhWrzydTVJPUWCCO7cNdjd7W8xr6kKhmWRSukoikrKMHHYWo/2Zgz+horGbBpTjSzdrLGmMsLg7O1vajwOjYDbTlVVFVlZWdSFYmTvYtnF5tF7E8syW43qd4U7uwLbpuGE4yEWL1jNyje+YtO6tn+JO/744/nFL37BiSee2Ov7LaiqgtfdP3aiFUII0Tf1eED/85//zK233sqVV15JdXU1hYWFXHbZZdx22209fSkhOlQbjBKNRkmlUgTcuzd6vmJLmH98Wk44Gac2WYdli5IzehGu9Ppdn9wJigK+/M14sioJbhpOY2UJCTPB16WQ0E1+NqUQ+3dWLFlfHWV1RYSI0QS2FN6C1R3UDoqiYNcgqZsYhkFKAZumthqdV+0p0geupn7NeHymn7nL67h0ausVW3ICdtZVhYnHE2yuDu4yoBuGicOuoSgqpt7+myTTtDAtiw0VjduPWRZs/YObFTNRNn9E46JKiLV+A+Lz+7nwgguYOXMmI0eO3GlbhBBCiO+THg/ofr+fBx98UJZVFHtVXTBKKBRCURR8ru7PDf7w23r++3U1MSNGXaoOmydI9uiF2FyxXZ/cRao9RcbQlbgyaqn7diK1KYvlm+HJeVu46MginPbmkG5aFp+sbiCZ0kkqMdw561F38fClqjQ/IKrrOpqmkkwZLau6bOPJ3UJoyxDCySbWVjmobGy9y2aG146mKtTX11Ht2/UTt5qmkul3U9GoYSZdWBZtduPcNq1lRxsqGqFahyVxlDUpLL31YzJZuQX8+NyLue7/rmDYoK4t+yiEEEJ8H/R4QBdib4sndaKJFE1NTfhc2k7nce/M16VB/vt1NSE9RDAVxJ1dSebwpaha96ZrdJY7s5rsMQuo/eZAapIWVoXFY+9v4tKji3E7NGqbkqytjBI3o1iqhTtnQ6fqtakKhmmip3QUlDZriSsK+Ao20rjeS7qVzidrggza4UunKgo+l42mpjBJ3SASS+50qoddU8nwu9BUO1ZKxUw60ZzbQ79pfuf5dN2CdUlYmoCK5jccO5aw5Q8lc9hRnHnCFKYfPQm3t2fnmAshhBB9Re9O1hRiL2iKNofAaDTa7Z1D11VFeeGLSsJ6mGAqSKB4XfMumL0czrdxpdeRM/ZLUmqY6mQNpTVRXvi8AsM0WV0RoSoYJ0UCu7sRzRnpVJ2KomDTVAzTaF6rXTfarEvuzd2CoumE9TALN4RIfGdg3ufSCEeap5o0hOM7vZ6mqWSnebApzeMAeqL1qHvL6HnQgE+j8HQjvBNpCecAqlsl/Yh0si44HO3Qk3DmDWdLY/P65t9djUYIIYToL2QEXfQ7oUgCwzBIJBJ4djFPuj2N0RSzPy4jkorRkGrAm7+JQMnqNtMzepsz0EjO+PnULD+UupTGsi0q7yyrpSqYRNd1dDWJN6O8S3VqChiKgp7SURUVw7SwaTvMRbcZeHPLCFc68Bt+NoYUJu9wvt9lo6w+Tiwep6EpRlHOzpdCLclNw645UFCIN2biDDSHcsvYOlq+LAGb2tm0IUsj56hM/Af4UR0qyXCCcD3oVopQrDnAd/cvI0IIIURfJwFd9DtNsWTL8ntdXfvcMC3+9nE5wXiCulQdrowaMoau3OPhfBuHt4nM4UuoXXkQIT3Em4tNfA6FFAlQLBzpXQvoiqJgU5t3QDXM5lF0TVVaLRXoySknXDGQpJmivKn1H9m8Tg1FUQg3NdHQlL7L600ZX8Lf3lmMXXERrc/Dm7aK0Jchgl8Gm0fOd6QCwxzkH5WFe4i71fQbzdncn4ZlEEk0nycj6EIIIforCeii3wlFEi0B3WXv2iyut5fWsqEmSl2yDsUZIWvEEhSlR/fy6jJ3Zg3+ovU0bh5CmuKgNqiDXUfVkmiuUJfr01QFw1QwdB1NbTuK7vAHUWw6CTNOWZPWsmvmtnPtmkIikSCe3PWuoMMGZFKcG6D2qwWEv/ycDdUbWlZo2caWaUMfZYcxToYMy2o3eKu2FIpmoFs6kURzBW5n/14rVwghxL5LArrod8KxJLF4HKdd6/SW9AB14STzvqknpIdIEidv5CJUezvTL/aCtJLVRGvzCIXd6LoD1ZbC5gl1e2RfU5UOR9EVxcKVXku83oNmeNlcF2do/vYwbNMUUrpOUt/5fPyamhr+9sRfWfLcwzTVVrZ+UQHvGC+BwwK4hroprWzcaV2K0jyKrscChLeOoHskoAshhOinJKCLfkXfGjpTySROW9fS61tLakkaOk1GE/4Bpd3egKg3KKpFoGg9NUvTsEwNHR2nq7Hb9e1qFN2VUUNDbT4ePKyujDI039/ymk1VMbY+YJrSDew7bHpkWRYffvghTzzxBP/+979JJpOtL+zykDHZRdqhAWzp23/8DCvK7MTXYNtDrQpel0OmuAghhOi3JKCLfiWxddpFKpVqs7nPzmyqi7FwQ4igHkSxJQgUre+tJnabohnYHCESSQcoBoa97RriXWFTFZLb3tDoBrYdvl7OQPMmTDo6FcHWIdumKeh6818WkqnmgF5RUcHs2bN5+umnWbt2bZtr5QweTyJ7LLG8TOxD12BLL+1ye01DQ0PB5bST7nN1+XwhhBDi+0ICuuhXEqnm6Q+pVAq3o3MjrJZl8drCGlJmiogeIX3IWlTbrudX70mmoYGpotoSoDbPwU5pQSzLavWAZ1eoqoJiKhiGsXUU3URTm0O6zRUDxcRQDKq/G9BVhbiuY+g6//3f/3jxuX/wxhtvYBitp7xkZWVx0UUXcda55/N5aYTfP/sh6PWENg3Hk1XZ5c2eTN2GXVFxOe3kZXi7dc9CCCHE94EEdNGvbJsXnUrp2N2dW8Hlm/II66qjNOqN2NwRfPmberOJ3WKmmjcEskwLRdWxAEtNEk+ZnV6pxrQsquqb1zDPy/ShKgo2VSFlGFiWjZRuojmaA7qiWNjcEYywi5qmFIZptcznr66q4OOPP+L+Lz+mvq6mzXWOO+44LrnkEk499VScTicAYTYyZXwJ8xalSJlxGtaPJXv0gk7PoTeSNoykE4fdQU66l5x0CehCCCH6Lwnool9JJHUsy0LXU9i1zj1E+P6KOuJmgrgRJ2vgahR1767a0h5Tt2MaFpZhQ7Gltgb0BLGkicuudn8UfetpumGgqEqrEXm7O0IynI5pWVTWh1mz/Gvmzp3LsmXL2tQzYMAALrroIi688EIGDx7c5vWRxVn86KhxLFpdhh5Jo6neIFJZgq+gc2+Goo3Nc9Rddi+jirNx2Lu3AZUQQgjxfSABXfQrpmW1LAvYmWcI68Mp1tfEiOhhbJ4w7qzKXZ+0F5i6HStlYlk2FMUExcJUY5iWSlK3cNo7vlnDNKluaL3bqGVZLasdamrzNBebzUbKMHFsfejT5g4TCVZS8+18fvXaEuKxaKs6NM3GjFNm8PNLLuH4449H0zoOzXmZPvIzfZwxdTxPvfk1bsVLw/oxaM4Y7sy2o/DfbWu4qgi74sSpOTj+4KE7LS+EEEJ830lAF/2KZW37H6ATAX3RxhCmZRIzYwRyyvfahkS7Yuo2rBRYlgaKBaoBqomFQkI3ce5kvffvhvPvHsvP9GGYJqZhoCsKWgKaFjfR+Pkn6NVNfHehyezcAiYdcxI/PvdCzjt5UqdH78cPySMYSbB6UxUfLbMwFYO6bw8gc+RiPFlVHZ4Xbkgn2ZhLpiud3AwfJx46vFPXE0IIIb6vJKCLfsWyrB3y+a6D48INIeJmHMuy8OR0bVfOPcmyVCzDRGHbzTX/t2lZpAyz3YdFd9xgaGcURUExIbYyQnJ5gsSaGHxniXOb3cGRR0xh+vTppLxFZGTnkpOT26WpNek+FyOLszjn+IOoDUZYuQlQFOq+OYBE4QbSSta0eTg3FnbTuGZ/nJobvz3AhSfsL8srCiGE6PckoIt+xQKsrSF2V9mxojFBRWOCiBHF4W/s8qoie5SpgmWA0jwxRTE1UIzm4G6BblrYtdY3vO2B0I7kZnjRK3WCbwWJLY9hRdsJ9Gk5ZA6dxBk/mM7JBxVjWRZfl4ZwOBw47V3/8TFsQCZN0SQzTz+Cx175lGWlYFPtRCoGE60ZgCe7vHmJR8Uk1hQgUjEIzfKQ7cnnoFEDuOikiV2+phBCCPF9IwFd9CuWZW2f4rILizY0T2+JGzHS+/ToeXPwtkxQFKP5XQgKimo1PzgKJHWLTj83GTFhtU79mjh6ddvlJFWfSuDAAI5hJdRXTcHvLkJzuAFI6CamZeF2e/B7HF2+F0VRmDg8H01VuOr0I/jvh0uZ83UpdsNNXA8TqXARKi9pLouKx+Yj05PDsMJsHrrqBBk9F0IIsU+QgC76FUVRUJTm+di7yulLNzcRNaKgWHiyK/ZA67rHMreGUhMUNQV6c1hWrOZVaqyt01ygdULPy/S1vF5dE4ZSHb7VYVNzyG8VzTVwjHTiHO/BO9KH220nGXJBFYCFaTZ/MaOJ5hF8j8eN3+Ps1v0oisKEYfn43A7stolMnjCMlz9cyrLSWgzTxMJE1TQcNgeapnLSocO565Jj8bg6tyqPEEII8X0nAV30K3ZNRdu6I6ZhdpzQEymT6lCSpJXE4Q2hOZIdlt3rrG1vOCwUJdUyt14xHShKHMtS0A0F07JQd5jXowCpshTRxVFYHoNE26rtRXY8+3twjXVhOZTmoK+CbpqYRnMgVlFxbV0fPZLQsTsc2O27v5vn0AGZFOUEWFNWz8D8dOqbYqwtq6eiLoxNUxmUn86MSSMYXJCxW9cRQgghvm8koIt+xW7TUBQFTdN2GtDLG+MAJM0kDl9oTzWve5Ttq9Koapxtz4laiQCKJ4JlNIdn3bBw2BT0Wp3Y0hix5TGMBqNNdWpAxTPBg3uCG1vW9h8B1tY/ORimiWqqWLoNBQVFUXBtXSUmnDDw+QIAux3QAZwOG+MG5zJucC7xpE4iqWO3abidtm6v7S6EEEJ830lAF/2K3dYcJFVNQ99JQK9oSDRPDbFSeL19O6Ar2x4MVRVULbZ9dZpEOoq3HBMwmwyiSxIEV8bRK9rOK1fsCq7RLtz7u3EMcrQbfhVFQVUUTNPEMi2MbQEdBY9DQzcswnGDkrwAHqcdl6Nnf3y4HLYer1MIIYT4PpLfhqJfsW2d3mLTNAzT7LDcloYEKSsFFjj6ekDfurOpooKqNY/8Y4EZ8kJZClYkMTYbtFmDRgHHYAfu8W5co12ozo7XSt9GVZqnt1iAnrS3vBlwOzQaos0romekZ5C/dX67EEIIIXqeBHTRr7TsgmmzoxvxDsuVN8SbAzpg9zbtkbbtDkU1QVVQrBhm1VqsytVQsxHaeRNiL7Q3h/KxLjR/Z5d2aaaqCpgmlmWix12oNId6n0ujPpzC6/PhcNgpyPL3yH0JIYQQoi0J6KJf2TZFwuF0kAhH2y1jWhbljQmSZhKbO4qqtZ2n3ZdYpkVicz2RRbUk1tdipdppb5qKbYyTjAN82LK7/22t0LzBk2mYpKIBbGgoCmR67ZQ3JCgpycTlsJHh3/3550IIIYRonwR00a9omorLYcPpdBJqaH+KSzhuoBsWuqVjc+98M5/dYZoW68sbABhSmNGlNbwt0yK+KU54SZjw0jBGUzuh3OFGGWXDGmui5tnRbDZs3t37lm6eh25h6GDEfTgtG7l+B+G4gWVZZGRkUpjllwc4hRBCiF4kAV30Ox6nHZfTRcowMUwL7TvBOL51BNq0LGy21B5vX0fB3bIsEpsSNC1tIrI0gh5s+7AnNhX7gGzMrEMxcvNR8lZC1lKwFEzT2roU4+6FZ0VR0OM+LEtBtTQK0h1UNCZIT0/H4bBTmC3TW4QQQojeJAFd9Dselx2ns3kTnYRu4nG0nocdSzaPrFuYqLZ2QvBu2rapj7nDTkmmZUE7A/qWZRHfnGgZKdcb22mPBp7hPhxDi1F8fhSSNDUUYykmVlMRZC/p9O6pnaEqYEQzwALV1Ehz24inDIYMGECm302G391j1xJCCCFEWxLQRb/jce4Q0FNtA3oi1ZyUTctE1Xo+oG8bHd/RhorGlv8emJ8G1TqsSbJ5fQi9oaNQ7sE3wYd3jBfVpRGtySVVn8KMGNgc9Zh6BlYiHSvhR7E3r+HSE1NPFAX0UCE27FiWgtuhEUhLw+f1MqI4a7frF0IIIcTOSUAX/Y7P7cDhaJ6THUsaZHhbbxFv7DjarHS8FGOPsiyoNWBNko1rGiHYfN1W0VxtHco1T+s3FqotierUMMJ27M4qUslM0ICGkZC7uOeaatrRw3m4TQc2xcTnUhlQOIAMv5ucdG+PXUcIIYQQ7ZOALvqdbTtcer1eIom2K7lsy+cWoCg9NzVkmyGFzVvTG6bJxsV1sC6JbYOBXtfOfHcFKLLBcAeDj8hD83a8LKLNFcNIpoGqY1PrUBQTxVSwgkOxsleA1jNvNlLBfBRTxWba8dpNXG4vfr+PEUUyei6EEELsCRLQRb/jcdmxaSpej5famrZrnG+fG97z4dwyLOIbYkSWRwgvD0Ow+YHUViPlCjCgOZQXT8rB7m/+NtzVKi82Z5SkkobmUTEjTpyuzcRjAzGxQ3AQStb6HrmHeH0JGjYMQyXgNcjNLyI7zUNuhoyeCyGEEHtCrwT0srIyrr/+et566y1isRgjRozgqaee4sADD+yNywnRiqIopHldeL1eKipMUrqJ3bZ9F023vXmUWkXF1O0dVdNplm4RXRNtDuUrw5iRdkayFXANduHfz497rIdNTc1vHOx+W6eXX1Q0E80Vw/S7MMImDlcFidggMGxY9aMhc+Nu34se85MK5uO23KiKRUF2GqrNxv7D8ne7biGEEEJ0To8H9IaGBiZPnszRRx/NW2+9RW5uLuvWrSM9Pb2nLyVEh9J9LrxeDwDhhEHGDgE9feta4ZqqoSe6tyKJmTCJrooSXh4m8k0EK9HOaPy2Bz3HbZ1T7mt+Y2CaFnRz81K7pwkj7kb1qFgxDZujmlRTCWherLqR4F/bvYq3ilaMRkVFNZwUBsDp9lCUE8Dt3P03MkIIIYTonB4P6Pfccw/FxcU888wzLccGDRrU05cRYqfSfS6cTid2u51IovWDomnu5v+2KTZSic7viGlEDSLfRIgsjxBdFcXS24Zyxa7gGdUcyj2jPGjutnPKVVVhWFFmN+4KNHsKzRnHnu4iETex2SrBHISacmLUjUHPr8Tm6t7mS6lwJomGIlymB5ddZWhRBk7VJOBxdqs+IYQQQnRPjwf0//3vfxx//PGcccYZfPjhhwwYMIArr7ySn//85z19KSE6lBloHhkPBAIEw0F2zMM2TSHgthHUNWKdHEGvn1tP/Xv17a5lrrpVvGO8eMd58YzwoNrVtoV6kMPfgJHKw55uI7nZiWI0oqaywGHQVHoI6SM+Quni8pGmbqep9BA0y4bddHHIiEwC/7+9ew2u6q77Bf5d973Xvt+yL7knJYRLASGUgtXWWjhFW7VV2047ip5zfJ6eoVbKOMe26kA72KovtC/qZdAzjr5g6gutOmPPHJlHW/Rp+0B5WstDebhIgEASdkJI9i37/j8vAoE0IcDTnb0X2d/PTGa6115Z65f++MM3a//Xf5k67Mggna3+w5yIiIjqWcUD+vHjx/GTn/wEW7duxdNPP429e/fi8ccfh2EY+OIXvzht/1wuh1wuN/k6kUgAAAqFAgqFygSDi8ep1PGocuaqN4oEmIYCh8OBeHwI47k8NOVScPbYFfQnFZTzBsolCZI8+wooakCdEs4VpwLHUgccSxywd9ohKZfmkYsKPjRoJpJcgu4YRa7kh5CckEUWiijDXnYikxEY+8etcHf+61V/pkv1AskTPSjlHHCUXIj5Tdzc7IaEMgbiCaTHs8jn8xVZY50qg3+nWRd7Y13sjXXVU2+u9WeURIXThK7r6Onpweuvvz657fHHH8e+ffvwxhtvTNt/+/bteOaZZ6Zt37VrF0zTrGRpVGf6zmXRdy6N3uPHEXEKuPRL7/3lpIIjo0WMSWPwLfl/UIz0rMcqZ8s493/OwVhgwNZtg9akQbrGmzvnSiEZQqK3BxhWoBZl2B0eFOQyMloGquc07E1vQJJLsx5DlGWM969G4XwHjIIDDtWG25rK6PQJDI9LkG0uRKNRrGx1Q1UY0ImIiD6ITCaDhx9+GGNjY3C73Vfcr+JX0KPRKBYvXjxl26JFi/Cb3/xmxv2feuopbN26dfJ1IpFAc3MzNmzYMGvh16NQKGD37t1Yv349NI03u1nJXPZmaDSNfzvUD6fDCYdaRHvo0nSWQXUY/YeGkMqloKEBdkd89oM5ANf/dlW0vg+qbB9H6h8O6B4PXIUslsR0vDukQIOGZFLG+HE/nK1vQXOem/H7SzkbEidvRTEdgENyw2E6sXFZEHct8cOuKzg6mMLBY3340IoVuKvnJpg2jh2r4N9p1sXeWBd7Y1311JuLM0WupuIB/cMf/jAOHz48ZduRI0fQ2to64/6GYUw+lv1ymqZVvElzcUyqjLnoTdjvhq7F4ff7MDIch6pe+uN+U9iBPYdHoUgqcqMhmIGhip67GkTRBiEk2DQNsZAfnU0yytJ5/H3QgEtSMZ5TkTh6OzT3WeiegQtBvYxC1oHcSCvyozHIQoVH9sFU7fjkihD+27LQ5JVyTVVQLpehKCogyRw7FsS/06yLvbEu9sa66qE31/rzVTygP/HEE1i3bh2ee+45PPDAA9i7dy927tyJnTt3VvpURLNSFBkBj4lRrxeDg4NIZYtw2ib+yN8UMSFLgF2xITsarHGl/zXZkQZIEuDQdHSEHQgFHfB6PGjwDuHN3jRE1ouClEVhVEdydOo65goUOCQH7KoDLpuOL380hpubp35ipcoSyuWJeeyFUmWeUkpERERXV/GAvnr1arz88st46qmn8Oyzz6K9vR0vvPACHnnkkUqfiuiqYgEX4udT0DQNI+nCZEC3aQraQnakBsaRGnegmLVDtY3XuNrrkx6KwabYoMoq7lzsR8Cp4/T5LFQ1ipZYEe/0juK9AQ3jeQcEyihLJQASFFmBJmmwGwpWt3uwcXkQfqc+7fiKLKF8IZgXGdCJiIiqZk6eJHrPPffgnnvumYtDE12XiN8JWZbh9fkwMjKMZr9tcjWShVEHjp2duDk0ez4IZ7SvlqVel2LWjnzCB79uIuzREfUakCQJnQ0mol4DI6kC/C4b1i4s4exYDqdGckhli1DkiSUmuyImbun0QFenr9N+kQRAYOIe8nJ5blemISIiokvmJKATWYWuKQh5TIwFAhiKx5HKluCyT/yx74468H//LsOQDWRHQzdUQM8MRyFJEuyyHSvb3FOWQDR1Bab/UvAulQVkCde9TOLlkZwrLBIREVXP3D5RhcgCGkNuuF0u6LqB4VT+0na/DQ5Dge3CPPRy4ca5MSUzFINdtkOWZKxsm321I0WW/ktrmAsAEia+j2ugExERVQ8DOs17Eb8TiiwjGAxgJFVA6cJ0DVmSsKLVBYfiAMoqUoMtNa702uRTLhTSLpiKidagHYEZ5o9XGuM5ERFR9TCg07ynKjIagy6EGhpQFsBw8tJV9DsW+aFKChyKA8n+NoiS9YfE2KkuKJIKm2zDqqtcPf9AxKUr57yCTkREVD3WTyNEFdAe9cHQdXi9XsQTlwJ6wKljeasLLsWFckFHOt5UwyqvLjvmR3akAV7NA6+p4ZZOz5ydqyzE5NNS5Ro/NZWIiKieMKBTXXA7DPhddoTDYYznS0iMFyffu3NxAKqswlRMJM50QAhrhlEhgLET3dBlHaZiYuPyIHR17oZwoSSgKhM3mxralVd7ISIiospiQKe60R71we12w2634+xYbnJ7k9+GrogDLtWFUtaOzFC0hlVe2fhwFPmkBx7Ni6jXQE/H3F09ByYCujIZ0LngExERUbUwoFPdiPidsOkqwuEIRjNFZAulyffuXOyHLuuwK3aMnuhGyWIruoiyjNGTC2FT7LDJBu79UAjyHM8LL5TKUBQVkgRoc3ilnoiIiKbiv7pUN2RZQlvEi2AwCFXTcOb8pavoCyImljQ64dN8QMGO0d7FNax0utHebpRzJryqB10RE90x55yfs1ASUFUFuqrwJlEiIqIqYkCnujJxs6iKWDSKkVRh8iq6JEn4/JoInLoGr+ZFJh5D2iJTXTJDUaQGWuFVvbCrOj69Kjzn5ywLgWJJQFFUGDrnnxMREVUTJ5ZSXVEVGZ0xH3L5IvoHBnDmfA6dDSYAwG1XcV9PGLveKCOrZHH+2FLozgQ0e7pm9eZTLowcWwpTMeFUnbivJ4yo15jz82YLZQgB6IYOl33uz0eze2jnGzibuPSJD4RAKq3ghSN/m/KY17DbwEv/tLYGFRIRUSUxoFPdaY/6cLz/PGKxGE6dPImYtwT7havEPR0eHBlMY+/xMvL5PIbfW4XQ0n+DauSuctTKK+ZsGD7UA02Y8Ok+rGpz49ab5vbG0IvGcxOfLBi6Dqc59w9CotmdTeTQO/z+XxQlDGUzNamHiIjmFqe4UN1RFRmdjX6EgiFomo7TI9kp7392dQRRrw1BLQiRdSN+YC2KWXtVayxm7Rg6uBrIOxHUg2gPmXhgTaRqc8HHC2XougZZUeBmQCciIqoqBnSqS20RL+yGhubmJpxPFzCWKUy+Z2gy/ucdTQi7TTQYDZByLsTfXYtCZu5vzAQmHkZ09u/rgHEvQnoQIZcN/+P2pqqupDKeL8Fun/ilhFNciIiIqosBneqSqshY3BZCIBCAy+XGyeEsykJMvh9w6vjq+hY0eidCulx0In5gDfLJuZ1ikhpowdB/3AKt7ELYCCPqMfHPdzbDaavubLRUrgS7aUKRJNgNzoQjIiKqJgZ0qltNITf8Ljva2lqRK5Zxdiw/5X2PqWHzXS1oCzjQoDdALTlx9t21E0seFiu7skm5qGLk2BKc/8cSOBUXQloIi2IubLm7DSFXdaeYZAslFIpluF0uOG1cYpGIiKjaeGmM6trS9gaMJMcRDofRHz+LgFODftlUEqdNxf+6qxk/f/U0pLMSkqUkEv0dSA/F4G37T5ihfnyQ/FouqkgOtCF1pg2ipMOneeFUnbh9kb8qDyOaSWK8CEmS4HS5MF7lK/dERETEgE51zuO0oS3iRbFYwrmREfQOjWNh1DFlH5um4J/vbMa/HBzBnw/KMBUTo4VRjBxZjtRgC5zh07D54lD0/BXOMl25oCE12IJkfztEUYdDccBtuKErKh5YE8Hqjuqs1jKTsUwRDqcTiqzAbeca6ERERNXGgE51r7sliMGRFNrb23Hk8GHEEzk0uKfeGKkpMu5eFsTqDjd+vz+O/zitIlvKIpEyMJLwARKgO0dh98dheM5B0XOQtTwkCAhIKOUN5BM+5JI+5BM+FDJOSJI0GcxVScHqDg/uWhpAsMpTWi5XFgKJ8SKiMQ90TYFkMKATERFVGwM61T1NVbC8M4JsvohQQwNODQ3BbVdh06aH04BTx3+/vQn/2Z/Cy2/FMZS0oSRKyJazGM/YkUj5IC672XTauWQNuqzDpRuwyTaokoKeC8G82nPNZzKWKaJUFvD5fAh5TAzEOf+ciIio2hjQiQA0+BxoDXtRKrcgkUjgeHwci2KOK94g2R1z4hv3OnBqOIv3zqRw8EwKA6M5CCFQEAWURRlllC9cP5cgQYYh65AlGRKARr8N7SE7blvos0Qwv2g4mYfpcMBut6Mx6MLA0VpXRMDEE0KnEAKpdBpOh2Pak0SJiOjGx4BOdMHithCGxzLo7OjAoUOHcOZ8Dk1+2xX3lyUJbSE72kJ2fGJFCOdSeRw6k8bgWA7pXAnpXAlCALIM6KqMloAN7SETzX4bDM16CygVSmWMZopoaYnB0FSEvGatS6ILXvqntVNeFwoFvPLKK/jEJ26Dpmk1qoqIiOYKAzrRBaoi40MLIvjXXAGNTU043dcHU1fgd15bAAo4ddy20DpXw6/XuVQBkCT4AwE0hdxcXpGIiKhGGNCJLuNz2bG4NQQhBDLpDI7HR2DTnTD1+X2zpBAC8bE8vF4vNFVFc4O71iURERHVLet9zk5UYx0xH5pCbrR3tMNmt+PoYBrF0pVv/JwPRlIFZAslxKIxBNwmXCbnMhMREdUKAzrRDJZ1hOF3mViwYAFKQsGxs2mUZ1md5UYmhED/aA4ejxcOh4mu5kCtSyIiIqprDOhEM1AUGau7Y3A5JkJ6KidwbDAzL0P6+XQR4/kSGhtj8LvsCHp4cygREVEtMaATXYHd0HDLokZ4PW4sWLAAY9kSeuPjs65zfqMplQX6Rsbh8XjhdDp59ZyIiMgCGNCJZuFz2XHLokb4vB50dnRiJF3AieHxWpdVMWfOZ1EoSWhtbUXAbSLkddS6JCIiorrHgE50FUGPiVULYwgE/Ghrb8dQIo/eocwNfyU9nSvh7FgescYYTLsNyzvDtS6JiIiIwGUWia5JxO/Eh26K4N/FxJNBe0/0olDMoDNsQpFvvPXCS2WB3ngGdtNENBJBV3MADvuNu4Y7ERHRfDLnV9Cff/55SJKELVu2zPWpiOZUY8iNVV0xNISC6FrQhWSujMMDaRRK5VqXdt16h8aRKwGdHR3wOGzojPlrXRIRERFdMKcBfd++fdi5cyeWLVs2l6chqppY0IU1i5sQ8HuxsLsb2aKEQ2fSGM+Xal3aNes/n8VIKo+Ojg64nA6s7IpCvgE/BSAiIpqv5iygp1IpPPLII/jZz34Gn883V6chqrqgx8SHl7Yg4PVg8eLFkFQd751J4VwqX+vSrupcMo/TI1k0NjbB5/Nh5YIoH0pERERkMXM2B33z5s345Cc/ibvuugs7duy44n65XA65XG7ydSKRAAAUCgUUCoWK1HLxOJU6HlXOjdobuy5jTXcUbx3px8KF3ThxohdH+kcQcmto9tssOS99KJnHiaEsAgE/wuEwOmNe+F3GFf/f36i9qQfsjXWxN9bF3lhXPfXmWn9GSczBUhQvvfQSduzYgbfeegs2mw133HEHVqxYgRdeeGHavtu3b8czzzwzbfuuXbtgmnxgCllbqSxwcngcw6kCEmNjiMeHoMplNJgCplbr6i45nwWGMxI8Hi8awg0IuXS0h+y1LouIiKiuZDIZPPzwwxgbG4Pb7b7ifhUP6H19fejp6cGf/vQnLF++HABmDegzXUFvbm7G8PDwrIVfj0KhgN27d2P9+vXQNAulJpo3vTkVH8PBE0NIpzM4ceIEkskU/E4VLX4bNLV2q5lOPIgoi6FEAZFoBM1NzWiPerGkLXTV750vvZmP2BvrYm+si72xrnrqTSKRQDAYvGpAr/gUl/379yMej2PVqlWT20qlEvbs2YMXX3wRuVwOiqJMvmcYBgxj+hxYTdMq3qS5OCZVxo3em87GIMJ+N945Ngin04mh4WH0nerDewPjaPTZEHLrVZ/2ks6V8I+z48iXgJtu6kQoFEJXUwALW4LXdZwbvTfzGXtjXeyNdbE31lUPvbnWn6/iAf3jH/84Dhw4MGXbl7/8ZXR3d+Mb3/jGlHBONJ847To+vLQZffEE3lMV+Lw+9J3uQ9/QEPpHc4h4dIQ9xpwH9UKpjIHRHM6O5WE3TSzp7ITTNLG0vQEtYc+cnpuIiIg+uIoHdJfLhaVLl07Z5nA4EAgEpm0nmm8kSUJL2IOI34n3Tg5BVRXEolH0DwzgzPAwBkZzCLl1BJ06TKOyv6yWygKDYzkMjuYASUY0FkMsGoPPZcfKriicfBARERHRDYFPEiWaA7qmYMVNEXREfTh6+hwMw0BjrBGDZwcxPDSMwdEk7LqCgFOD16HBrsmQpOu/sl4WAsnxIs6lChhJFSAkCeGGMKKxGAxNQ2ejH11NAa5zTkREdAOpSkB/9dVXq3EaIstxOwysWhhD93gex86MwDB0NDc1YSyRwLnhYQyMjuL0SBaKLMFhqHDaFNh1GZoiQ1MkaIoMSZq4Ol4WAqUyMJ4vIZMvIZMrIZ0roVQWMGw2xBobEQyGYBg6Who86GoOwKbzd3AiIqIbDf/1JqoCh13H8psiWNQaQv+5JM4MmfB6PCiVy0inUkhd+Ion0ygWs1c9nmEYME0XogEHvF4vTNOEpiqIBVzojPng4HQWIiKiGxYDOlEV6ZqCtogXbREvxnMF9A8nMZJ043wyi1yhCAAoFksoFAtTHtalyDJkRYEsy7AZNqjqxPx1Q1MR9JiIBpxo8DqgKLVb0pGIiIgqgwGdqEbsxsQc8c4LrzPZAkZTWYznCsgVSsjmi8gXSwAARZagyDIUWYJp0+Bx2OBxGDA4hYWIiGje4b/uRBZh2jSYtvm9/isRERFdHT8PJyIiIiKyEAZ0IiIiIiILYUAnIiIiIrIQBnQiIiIiIgthQCciIiIishAGdCIiIiIiC2FAJyIiIiKyEAZ0IiIiIiILYUAnIiIiIrIQBnQiIiIiIgthQCciIiIishAGdCIiIiIiC1FrXcD7CSEAAIlEomLHLBQKyGQySCQS0DStYselD469sS72xrrYG+tib6yLvbGueurNxXx7Me9eieUCejKZBAA0NzfXuBIiIiIiospLJpPweDxXfF8SV4vwVVYul9Hf3w+XywVJkipyzEQigebmZvT19cHtdlfkmFQZ7I11sTfWxd5YF3tjXeyNddVTb4QQSCaTiMVikOUrzzS33BV0WZbR1NQ0J8d2u93zvvE3KvbGutgb62JvrIu9sS72xrrqpTezXTm/iDeJEhERERFZCAM6EREREZGF1EVANwwD27Ztg2EYtS6F3oe9sS72xrrYG+tib6yLvbEu9mY6y90kSkRERERUz+riCjoRERER0Y2CAZ2IiIiIyEIY0ImIiIiILIQBnYiIiIjIQuouoLe1tUGSpClfTz75ZK3Lqks//vGP0d7eDpvNhlWrVuGvf/1rrUuqe9u3b582PiKRSK3Lqkt79uzBvffei1gsBkmS8Lvf/W7K+0IIbN++HbFYDHa7HXfccQcOHjxYm2LrzNV686UvfWnaOLr11ltrU2ydef7557F69Wq4XC40NDTgM5/5DA4fPjxlH46d2riW3nDsXFJ3AR0Ann32WQwMDEx+fetb36p1SXXn17/+NbZs2YJvfvObePvtt/GRj3wEGzduxKlTp2pdWt1bsmTJlPFx4MCBWpdUl9LpNJYvX44XX3xxxve///3v4wc/+AFefPFF7Nu3D5FIBOvXr0cymaxypfXnar0BgLvvvnvKOHrllVeqWGH9eu2117B582a8+eab2L17N4rFIjZs2IB0Oj25D8dObVxLbwCOnUmizrS2toof/vCHtS6j7t1yyy3i0UcfnbKtu7tbPPnkkzWqiIQQYtu2bWL58uW1LoPeB4B4+eWXJ1+Xy2URiUTEd7/73clt2WxWeDwe8dOf/rQGFdav9/dGCCE2bdokPv3pT9ekHpoqHo8LAOK1114TQnDsWMn7eyMEx87l6vIK+ve+9z0EAgGsWLEC3/nOd5DP52tdUl3J5/PYv38/NmzYMGX7hg0b8Prrr9eoKrro6NGjiMViaG9vx0MPPYTjx4/XuiR6n97eXgwODk4ZQ4Zh4Pbbb+cYsohXX30VDQ0N6Orqwle+8hXE4/Fal1SXxsbGAAB+vx8Ax46VvL83F3HsTFBrXUC1fe1rX8PKlSvh8/mwd+9ePPXUU+jt7cXPf/7zWpdWN4aHh1EqlRAOh6dsD4fDGBwcrFFVBABr1qzBr371K3R1deHs2bPYsWMH1q1bh4MHDyIQCNS6PLrg4jiZaQydPHmyFiXRZTZu3IjPf/7zaG1tRW9vL7797W/jzjvvxP79+/mkxCoSQmDr1q247bbbsHTpUgAcO1YxU28Ajp3LzYuAvn37djzzzDOz7rNv3z709PTgiSeemNy2bNky+Hw+fO5zn5u8qk7VI0nSlNdCiGnbqLo2btw4+d8333wz1q5di87OTvzyl7/E1q1ba1gZzYRjyJoefPDByf9eunQpenp60Nraij/+8Y+4//77a1hZfXnsscfw7rvv4m9/+9u09zh2autKveHYuWReBPTHHnsMDz300Kz7tLW1zbj94t3Bx44dY0CvkmAwCEVRpl0tj8fj065qUG05HA7cfPPNOHr0aK1LoctcXFlncHAQ0Wh0cjvHkDVFo1G0trZyHFXRV7/6VfzhD3/Anj170NTUNLmdY6f2rtSbmdTz2JkXc9CDwSC6u7tn/bLZbDN+79tvvw0AUwYqzS1d17Fq1Srs3r17yvbdu3dj3bp1NaqKZpLL5XDo0CGOD4tpb29HJBKZMoby+Txee+01jiELOnfuHPr6+jiOqkAIgcceewy//e1v8ec//xnt7e1T3ufYqZ2r9WYm9Tx25sUV9Gv1xhtv4M0338THPvYxeDwe7Nu3D0888QQ+9alPoaWlpdbl1ZWtW7fiC1/4Anp6erB27Vrs3LkTp06dwqOPPlrr0ura17/+ddx7771oaWlBPB7Hjh07kEgksGnTplqXVndSqRSOHTs2+bq3txfvvPMO/H4/WlpasGXLFjz33HNYsGABFixYgOeeew6maeLhhx+uYdX1Ybbe+P1+bN++HZ/97GcRjUZx4sQJPP300wgGg7jvvvtqWHV92Lx5M3bt2oXf//73cLlck5/Uejwe2O12SJLEsVMjV+tNKpXi2LlcDVeQqbr9+/eLNWvWCI/HI2w2m1i4cKHYtm2bSKfTtS6tLv3oRz8Sra2tQtd1sXLlyilLLVFtPPjggyIajQpN00QsFhP333+/OHjwYK3Lqkt/+ctfBIBpX5s2bRJCTCwXt23bNhGJRIRhGOKjH/2oOHDgQG2LrhOz9SaTyYgNGzaIUCgkNE0TLS0tYtOmTeLUqVO1LrsuzNQXAOIXv/jF5D4cO7Vxtd5w7EwlCSFENX8hICIiIiKiK5sXc9CJiIiIiOYLBnQiIiIiIgthQCciIiIishAGdCIiIiIiC2FAJyIiIiKyEAZ0IiIiIiILYUAnIiIiIrIQBnQiIiIiIgthQCciIiIishAGdCIiIiIiC2FAJyIiIiKyEAZ0IiIiIiIL+f+1z31XxdiBIgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final P: [0.022 0.045 0.   ]\n"
     ]
    }
   ],
   "source": [
    "ekf = run_localization(\n",
    "    landmarks[0:2], std_vel=1.e-10, std_steer=1.e-10,\n",
    "    std_range=1.4, std_bearing=.05)\n",
    "print('Final P:', ekf.P.diagonal())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The estimate quickly diverges from the robot's path after passing the landmarks. The covariance also grows quickly. Let's see what happens with only one landmark:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final P: [0.263 0.798 0.004]\n"
     ]
    }
   ],
   "source": [
    "ekf = run_localization(\n",
    "    landmarks[0:1], std_vel=1.e-10, std_steer=1.e-10,\n",
    "    std_range=1.4, std_bearing=.05)\n",
    "print('Final P:', ekf.P.diagonal())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you probably suspected, one landmark produces a very bad result. Conversely, a large number of landmarks allows us to make very accurate estimates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final P: [0.008 0.009 0.001]\n"
     ]
    }
   ],
   "source": [
    "landmarks = array([[5, 10], [10,  5], [15, 15], [20,  5], [15, 10], \n",
    "                   [10,14], [23, 14], [25, 20], [10, 20]])\n",
    "\n",
    "ekf = run_localization(\n",
    "    landmarks, std_vel=0.1, std_steer=np.radians(1),\n",
    "    std_range=0.3, std_bearing=0.1, ylim=(0, 21))\n",
    "print('Final P:', ekf.P.diagonal())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Discussion\n",
    "\n",
    "I said that this was a real problem, and in some ways it is. I've seen alternative presentations that used robot motion models that led to simpler Jacobians. On the other hand, my model of the movement is also simplistic in several ways. First, it uses a bicycle model. A real car has two sets of tires, and each travels on a different radius. The wheels do not grip the surface perfectly. I also assumed that the robot responds instantaneously to the control input. Sebastian Thrun writes in *Probabilistic Robots* that this simplified model is justified because the filters perform well when used to track real vehicles. The lesson here is that while you have to have a reasonably accurate nonlinear model, it does not need to be perfect to operate well. As a designer you will need to balance the fidelity of your model with the difficulty of the math and the CPU time required to perform the linear algebra. \n",
    "\n",
    "Another way in which this problem was simplistic is that we assumed that we knew the correspondance between the landmarks and measurements. But suppose we are using radar - how would we know that a specific signal return corresponded to a specific building in the local scene? This question hints at SLAM algorithms - simultaneous localization and mapping. SLAM is not the point of this book, so I will not elaborate on this topic. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## UKF vs EKF\n",
    "\n",
    "\n",
    "In the last chapter I used the UKF to solve this problem. The difference in implementation should be very clear. Computing the Jacobians for the state and measurement models was not trivial despite a rudimentary motion model. A different problem could result in a Jacobian which is difficult or impossible to derive analytically. In contrast, the UKF only requires you to provide a function that computes the system motion model and another for the measurement model. \n",
    "\n",
    "There are many cases where the Jacobian cannot be found analytically. The details are beyond the scope of this book, but you will have to use numerical methods to compute the Jacobian. That undertaking is not trivial, and you will spend a significant portion of a master's degree at a STEM school learning techniques to handle such situations. Even then you'll likely only be able to solve problems related to your field - an aeronautical engineer learns a lot about Navier Stokes equations, but not much about modelling chemical reaction rates. \n",
    "\n",
    "So, UKFs are easy. Are they accurate? In practice they often perform better than the EKF. You can find plenty of research papers that prove that the UKF outperforms the EKF in various problem domains. It's not hard to understand why this would be true. The EKF works by linearizing the system model and measurement model at a single point, and the UKF uses $2n+1$ points.\n",
    "\n",
    "Let's look at a specific example. Take $f(x) = x^3$ and pass a Gaussian distribution through it. I will compute an accurate answer using a monte carlo simulation. I generate 50,000 points randomly distributed according to the Gaussian, pass each through $f(x)$, then compute the mean and variance of the result. \n",
    "\n",
    "The EKF linearizes the function by taking the derivative to find the slope at the evaluation point $x$. This slope becomes the linear function that we use to transform the Gaussian. Here is a plot of that."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "actual mean=1.30, std=1.14\n",
      "EKF    mean=1.00, std=0.95\n"
     ]
    }
   ],
   "source": [
    "import kf_book.nonlinear_plots as nonlinear_plots\n",
    "nonlinear_plots.plot_ekf_vs_mc()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The EKF computation is rather inaccurate. In contrast, here is the performance of the UKF:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "actual mean=1.30, std=1.12\n",
      "UKF    mean=1.30, std=1.08\n"
     ]
    }
   ],
   "source": [
    "nonlinear_plots.plot_ukf_vs_mc(alpha=0.001, beta=3., kappa=1.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we can see that the computation of the UKF's mean is accurate to 2 decimal places. The standard deviation is slightly off, but you can also fine tune how the UKF computes the distribution by using the $\\alpha$, $\\beta$, and $\\gamma$ parameters for generating the sigma points. Here I used $\\alpha=0.001$, $\\beta=3$, and $\\gamma=1$. Feel free to modify them to see the result. You should be able to get better results than I did. However, avoid over-tuning the UKF for a specific test. It may perform better for your test case, but worse in general."
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
